Blueprint Bibliography🔗

Bibliography (11)

• [Ati70] Michael F. Atiyah. Resolution of singularities and division of distributions. Communications on Pure and Applied Mathematics, 23(2):145–150, 1970. doi:10.1002/cpa.3160230202.
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  • Document root
  • Chapter 1: Introduction, Section 1.4: The resolution theorems of the library
  • Chapter 4: Main theorems, Section 4.1: Resolution of singularities in Mathlib's language
  • Chapter 4: Main theorems, Section 4.1.2: Local monomialization of a real-analytic function, Theorem 4.1.2.2
  • Chapter 4: Main theorems, Section 4.1.2: Local monomialization of a real-analytic function, Theorem 4.1.2.2 - Cites footnote 2
• [BG69] I. N. Bernshtein, S. I. Gel'fand. Meromorphic property of the functions P^λ. Functional Analysis and Its Applications, 3(1):68–69, 1969. doi:10.1007/BF01078276.
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  • Chapter 4: Main theorems, Section 4.1.2: Local monomialization of a real-analytic function, Theorem 4.1.2.2
• [BM88] Edward Bierstone, Pierre D. Milman. Semianalytic and subanalytic sets. Publications Mathématiques de l'IHÉS, 67:5–42, 1988. doi:10.1007/BF02699126.
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  • Chapter 3: Analytic geometry, Section 3.1: Ideal sheaves, submanifolds and blow-ups - Cites Definition 4.1
  • Chapter 3: Analytic geometry, Section 3.1.4: Closed submanifolds and blow-ups, Definition 3.1.4.2 - Cites Definition 4.1
  • Chapter 3: Analytic geometry, Section 3.1.6: The Jacobian ideal and analytic isomorphisms, Definition 3.1.6.1 - Cites Definition 4.1
• [BM97] Edward Bierstone, Pierre D. Milman. Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant. Inventiones Mathematicae, 128:207–302, 1997. Item numbers follow the arXiv version. doi:10.1007/s002220050141, arXiv:alg-geom/9508005, URL: https://arxiv.org/abs/alg-geom/9508005.
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  • Document root
  • Chapter 3: Analytic geometry, Section 3.3.2: Local models and quotients, Definition 3.3.2.2 - Cites §3
  • Chapter 3: Analytic geometry, Section 3.1.4: Closed submanifolds and blow-ups, Definition 3.1.4.3 - Cites §3
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.1 - Cites Theorem 1.10
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Theorem 1.6
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Theorem 1.10
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites after (1.2)
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Theorem 1.10
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Proof for Theorem 4.3.4.6 - Cites Proposition 3.13
  • Chapter 4: Main theorems, Section 4.1.2: Local monomialization of a real-analytic function, Theorem 4.1.2.2 - Cites Theorem 1.10
  • Chapter 4: Main theorems, Section 4.1.2: Local monomialization of a real-analytic function, Theorem 4.1.2.2 - Cites the sentence after Theorem 1.10
• [Hau14] Herwig Hauser. Blowups and resolution. In The Resolution of Singular Algebraic Varieties, volume 20 of Clay Mathematics Proceedings, pages 1–80. American Mathematical Society, 2014. arXiv:1404.1041, URL: https://arxiv.org/abs/1404.1041.
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  • Chapter 2: Schemes, Section 2.2: The blow-up along an ideal sheaf - Cites Definition 4.4
  • Chapter 2: Schemes, Section 2.2.2: Gluing the affine blow-ups, Definition 2.2.2.2 - Cites Definition 4.4
  • Chapter 2: Schemes, Section 2.2.3: The universal property, Definition 2.2.3.1 - Cites Theorem 4.18 (a)
  • Chapter 2: Schemes, Section 2.2.4: Transforms along a blow-up, Definition 2.2.4.1 - Cites Definition 6.8
  • Chapter 2: Schemes, Section 2.2.4: Transforms along a blow-up, Definition 2.2.4.1 - Cites Definition 6.2
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Definition 4.1.1.2 - Cites Definition 4.4
• [Hir64] Heisuke Hironaka. Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Annals of Mathematics (2), 79:109–203 and 205–326, 1964. Part II: doi:10.2307/1970547. doi:10.2307/1970486.
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  • Document root
  • Chapter 3: Analytic geometry, Section 3.3: Analytic spaces - Cites Ch. 0, §1
  • Chapter 3: Analytic geometry, Section 3.3.2: Local models and quotients, Definition 3.3.2.2 - Cites Ch. 0, §1
  • Chapter 3: Analytic geometry, Section 3.3.3: Analytic spaces and their morphisms, Definition 3.3.3.1 - Cites Ch. 0, §1, p. 121
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.1 - Cites Definition 2, p. 141
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.1 - Cites Definition 2, p. 141
  • Chapter 1: Introduction, Section 1.1: Resolution of singularities
  • Chapter 2: Schemes, Section 2.2.2: Gluing the affine blow-ups, Definition 2.2.2.2 - Cites Ch. 0, §2
  • Chapter 2: Schemes, Section 2.2.2: Gluing the affine blow-ups, Definition 2.2.2.2 - Cites Ch. 0, §2
  • Chapter 2: Schemes, Section 2.2.4: Transforms along a blow-up, Definition 2.2.4.1 - Cites Ch. 0, §5, p. 142
  • Chapter 2: Schemes, Section 2.2.5: The exceptional divisor and the push-forward of a blow-up, Definition 2.2.5.2 - Cites Ch. 0, §2, pp. 129–130
  • Chapter 2: Schemes, Section 2.1.1: Algebraic k-schemes, Definition 2.1.1.2 - Cites Ch. 0, §1, pp. 118–119
  • Chapter 2: Schemes, Section 2.1.2: Regular points and the singular locus, Definition 2.1.2.1 - Cites Introduction, p. 112
  • Chapter 4: Main theorems, Section 4.2: Algebraic schemes - Cites pp. 132–133
  • Chapter 4: Main theorems, Section 4.2.1: Main Theorem II: order reduction, Definition 4.2.1.1 - Cites Main Theorem II (i), Main Theorem II(N) (1); Corollary 1, "non-singular irreducible centers D(i)", p. 143
  • Chapter 4: Main theorems, Section 4.2.1: Main Theorem II: order reduction, Definition 4.2.1.1 - Cites Main Theorem II (iii) and the first half of (iv); Main Theorem II(N) (3) and the first half of (4)
  • Chapter 4: Main theorems, Section 4.2.1: Main Theorem II: order reduction, Theorem 4.2.1.2 - Cites p. 151; ℬ defined on p. 161
  • Chapter 4: Main theorems, Section 4.2.2: Main Theorem II(N): principalization, Theorem 4.2.2.1 - Cites Ch. I, p. 162
  • Chapter 4: Main theorems, Section 4.2.2: Main Theorem II(N): principalization, Theorem 4.2.2.1 - Cites p. 176
  • Chapter 4: Main theorems, Section 4.2.2: Main Theorem II(N): principalization, Proof for Theorem 4.2.2.1 - Cites pp. 176–177
  • Chapter 4: Main theorems, Section 4.2.3: Corollary 1: trivialization of a system of ideal sheaves, Definition 4.2.3.1 - Cites Corollary 1 (1)
  • Chapter 4: Main theorems, Section 4.2.8: Main Theorem I, Theorem 4.2.8.1 - Cites p. 112
  • Chapter 4: Main theorems, Section 4.2.8: Main Theorem I, Theorem 4.2.8.1 - Cites pp. 132–133
  • Chapter 4: Main theorems, Section 4.2.8: Main Theorem I, Proof for Theorem 4.2.8.1 - Cites pp. 132–133
  • Chapter 4: Main theorems, Section 4.2.9: Main Theorem I, weak form, Theorem 4.2.9.1 - Cites p. 112
  • Chapter 4: Main theorems, Section 4.2.9: Main Theorem I, weak form, Proof for Theorem 4.2.9.1 - Cites p. 132
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Definition 4.3.1.1 - Cites Main Theorem II′(N) (iii) and the first half of (iv)
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Definition 4.3.1.1 - Cites Main Theorem II′(N) (ii)
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Theorem 4.3.1.2 - Cites Definition 2, p. 141
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Theorem 4.3.1.2 - Cites p. 155
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Theorem 4.3.1.2 - Cites Definition 2, p. 141
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Theorem 4.3.5.5 - Cites Introduction
  • Chapter 4: Main theorems, Section 4.3.6: Resolution of a reduced complex-analytic space, Theorem 4.3.6.1 - Cites Introduction
• [Kol07] János Kollár. Lectures on Resolution of Singularities. Volume 166 of Annals of Mathematics Studies. Princeton University Press, 2007. The arXiv text (v3) is the resolution chapter, circulated as a Seattle lecture; item numbers follow it. arXiv:math/0508332, URL: https://arxiv.org/abs/math/0508332v3.
  Cited from (132)

  • Document root
  • Document root - Cites Theorem 45
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.1 - Cites Definition 24 (4)
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.1 - Cites Definition 24
  • Chapter 3: Analytic geometry, Section 3.2.1: Finite successions of monoidal transformations, Definition 3.2.1.3 - Cites Definition 30.2
  • Chapter 3: Analytic geometry, Section 3.2.5: Push-forward along a closed embedding, Definition 3.2.5.1 - Cites Definition 30.3
  • Chapter 3: Analytic geometry, Section 3.2.5: Push-forward along a closed embedding, Definition 3.2.5.1 - Cites 34.3
  • Chapter 3: Analytic geometry, Section 3.2.5: Push-forward along a closed embedding, Definition 3.2.5.1 - Cites Definition 30.3
  • Chapter 1: Introduction, Section 1.1: Resolution of singularities - Cites (3)
  • Chapter 1: Introduction, Section 1.2: Principalization - Cites §3
  • Chapter 1: Introduction, Section 1.3: Functorial resolution - Cites Theorems 35 and 36
  • Chapter 2: Schemes, Section 2.4.1: Finite successions of blow-ups - Cites Definition 29
  • Chapter 2: Schemes, Section 2.4.1: Finite successions of blow-ups, Definition 2.4.1.1 - Cites Warning 20
  • Chapter 2: Schemes, Section 2.4.1: Finite successions of blow-ups, Definition 2.4.1.2 - Cites Definition 30.2
  • Chapter 2: Schemes, Section 2.4.2: Divisor families and simple normal crossings, Definition 2.4.2.1 - Cites 34.1
  • Chapter 2: Schemes, Section 2.4.2: Divisor families and simple normal crossings, Definition 2.4.2.2 - Cites Definition 24 (1)–(3)
  • Chapter 2: Schemes, Section 2.4.2: Divisor families and simple normal crossings, Definition 2.4.2.2 - Cites Definition 24 (4)
  • Chapter 2: Schemes, Section 2.4.2: Divisor families and simple normal crossings, Definition 2.4.2.3 - Cites Theorem 35 (2)
  • Chapter 2: Schemes, Section 2.4.2: Divisor families and simple normal crossings, Definition 2.4.2.3 - Cites Definition 24
  • Chapter 2: Schemes, Section 2.4.2: Divisor families and simple normal crossings, Definition 2.4.2.3 - Cites (3)
  • Chapter 2: Schemes, Section 2.4.2: Divisor families and simple normal crossings, Definition 2.4.2.4 - Cites Definitions 25 and 65
  • Chapter 2: Schemes, Section 2.4.3: Operations on successions, Definition 2.4.3.1 - Cites Definition 30.1
  • Chapter 2: Schemes, Section 2.4.3: Operations on successions, Definition 2.4.3.1 - Cites 32 and 34.1
  • Chapter 2: Schemes, Section 2.4.3: Operations on successions, Definition 2.4.3.1 - Cites Definition 30.3
  • Chapter 2: Schemes, Section 2.4.4: Blow-up sequence functors - Cites 31 and 34
  • Chapter 2: Schemes, Section 2.4.4: Blow-up sequence functors, Definition 2.4.4.1 - Cites Definition 31
  • Chapter 2: Schemes, Section 2.3: Projective morphisms - Cites (2) and (3)
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Example 28.1
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites (2) and (3); Theorem 27
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Example 28.1
  • Chapter 2: Schemes, Section 2.2: The blow-up along an ideal sheaf - Cites Notation 19
  • Chapter 2: Schemes, Section 2.2.2: Gluing the affine blow-ups, Definition 2.2.2.2 - Cites Notation 19
  • Chapter 2: Schemes, Section 2.2.3: The universal property - Cites Notation 19
  • Chapter 2: Schemes, Section 2.2.3: The universal property - Cites Warning 23
  • Chapter 2: Schemes, Section 2.2.3: The universal property, Definition 2.2.3.1 - Cites Warning 20
  • Chapter 2: Schemes, Section 2.2.3: The universal property, Definition 2.2.3.1 - Cites Definition 30, 30.1
  • Chapter 2: Schemes, Section 2.2.4: Transforms along a blow-up, Definition 2.2.4.1 - Cites Definition 60
  • Chapter 2: Schemes, Section 2.2.5: The exceptional divisor and the push-forward of a blow-up, Definition 2.2.5.1 - Cites Definition 30, 30.2 and 30.3
  • Chapter 2: Schemes, Section 2.2.5: The exceptional divisor and the push-forward of a blow-up, Definition 2.2.5.2 - Cites Definition 30, 30.2
  • Chapter 2: Schemes, Section 2.2.5: The exceptional divisor and the push-forward of a blow-up, Definition 2.2.5.2 - Cites 58 and Definition 60
  • Chapter 2: Schemes, Section 2.1.3: Stalks and orders of ideal sheaves, Definition 2.1.3.1 - Cites Theorem 35
  • Chapter 2: Schemes, Section 2.1.3: Stalks and orders of ideal sheaves, Definition 2.1.3.2 - Cites Definition 47
  • Chapter 2: Schemes, Section 2.1.4: Invertible ideal sheaves, Definition 2.1.4.1 - Cites Warning 20
  • Chapter 4: Main theorems, Section 4.2: Algebraic schemes - Cites Theorem 68
  • Chapter 4: Main theorems, Section 4.2.1: Main Theorem II: order reduction, Proof for Theorem 4.2.1.2 - Cites Theorem 68
  • Chapter 4: Main theorems, Section 4.2.1: Main Theorem II: order reduction, Proof for Theorem 4.2.1.2 - Cites Definition 66
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Definition 4.2.4.1 - Cites 34.1
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Definition 4.2.4.2 - Cites Theorem 35 (1)
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization - Cites 34.1
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization - Cites Proposition 37
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Definition 4.2.4.3 - Cites 34.1
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Definition 4.2.4.4 - Cites 34.2
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Definition 4.2.4.5 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites 30.1
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites 32
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites 30.3
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites 72
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites Theorem 107
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites 111
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites Theorem 107
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites Notation 64
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Proof for Theorem 4.2.4.6 - Cites 72
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Proof for Theorem 4.2.4.6 - Cites Theorem 69
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Proof for Theorem 4.2.4.6 - Cites 32
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Definition 4.2.6.1 - Cites Notation 64 (1)
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Definition 4.2.6.2 - Cites (2)
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Definition 4.2.6.2 - Cites (3)
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution - Cites (4)
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution - Cites 34
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution - Cites Example 3.4
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Theorem 4.2.6.3 - Cites Notation 64
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Theorem 4.2.6.3 - Cites (3)
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Proof for Theorem 4.2.6.3 - Cites Corollary 22
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Proof for Theorem 4.2.6.3 - Cites Proposition 37 and Warning 38
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Proof for Theorem 4.2.6.3 - Cites Lemma 39
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Proof for Theorem 4.2.6.3 - Cites Lemma 41
  • Chapter 4: Main theorems, Section 4.2.7: Strong resolution of a variety, Theorem 4.2.7.1 - Cites (3)
  • Chapter 4: Main theorems, Section 4.2.7: Strong resolution of a variety, Theorem 4.2.7.1 - Cites Corollary 22
  • Chapter 4: Main theorems, Section 4.2.7: Strong resolution of a variety, Theorem 4.2.7.1 - Cites 30.2
  • Chapter 4: Main theorems, Section 4.2.7: Strong resolution of a variety, Theorem 4.2.7.1 - Cites Warning 23
  • Chapter 4: Main theorems, Section 4.2.10: Embedded desingularization with smooth centres, Theorem 4.2.10.4 - Cites 34.2
  • Chapter 4: Main theorems, Section 4.2.10: Embedded desingularization with smooth centres, Theorem 4.2.10.4 - Cites 34 and Claim 71.2
  • Chapter 4: Main theorems, Section 4.2.10: Embedded desingularization with smooth centres, Proof for Theorem 4.2.10.4 - Cites Theorem 69
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Theorem 4.3.1.2 - Cites Definition 24
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Proof for Theorem 4.3.1.2 - Cites Theorem 103
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Proof for Theorem 4.3.1.2 - Cites Theorem 107
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Theorem 35
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Theorem 35 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.3 - Cites Definition 31
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.4 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.4 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.6 - Cites Theorem 35 (5)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.6 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.6 - Cites Theorem 35 (5)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.6 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 35
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 35 (5)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites 72
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 107 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 103 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 35 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 35
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites 44
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites 34.1
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites 34.2
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites 72
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites Theorem 107
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites 111
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites 72
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites Theorem 107 (2)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites 72
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites Theorem 107 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites Theorem 103
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites Theorem 103 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Proof for Theorem 4.3.3.7 - Cites 108
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.2 - Cites 32
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.5 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.5 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites 34.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites 32
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Proof for Theorem 4.3.4.6 - Cites Theorem 103
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Proof for Theorem 4.3.4.6 - Cites Theorem 107
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Proof for Theorem 4.3.4.6 - Cites 34.1
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.1 - Cites (2)
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.1 - Cites (3)
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.2 - Cites Warning 23
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.3 - Cites Theorem 45
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Theorem 4.3.5.5 - Cites (2), (3)
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Theorem 4.3.5.5 - Cites Theorem 36, proof; Proposition 37
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Theorem 4.3.5.5 - Cites Warning 23
  • Chapter 4: Main theorems, Section 4.3.6: Resolution of a reduced complex-analytic space, Theorem 4.3.6.1 - Cites Theorem 45 (1)–(4)
• [TSPA] The Stacks Project Authors. The Stacks Project. Cited by tag. URL: https://stacks.math.columbia.edu.
  Cited from (39)

  • Chapter 5: Appendix, Section 5.1.1: Dictionary
  • Chapter 2: Schemes, Section 2.3.1: The symmetric algebra and the projective bundle of a module, Definition 2.3.1.2 - Cites Tag 01N2
  • Chapter 2: Schemes, Section 2.3.2: The projective bundle of a quasi-coherent sheaf - Cites Tags 01I9 and 01IA
  • Chapter 2: Schemes, Section 2.3.2: The projective bundle of a quasi-coherent sheaf - Cites Tags 01I9 and 01IA
  • Chapter 2: Schemes, Section 2.3.2: The projective bundle of a quasi-coherent sheaf, Definition 2.3.2.1 - Cites Tag 01OB
  • Chapter 2: Schemes, Section 2.3.2: The projective bundle of a quasi-coherent sheaf, Definition 2.3.2.1 - Cites Tag 01LH
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 01W8
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 087S
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 01WC
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 02NS
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 080B
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 01W8
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 087S
  • Chapter 2: Schemes, Section 2.3.3: Projective morphisms, Definition 2.3.3.1 - Cites Tag 01W8
  • Chapter 2: Schemes, Section 2.2: The blow-up along an ideal sheaf - Cites Tag 01OF
  • Chapter 2: Schemes, Section 2.2.2: Gluing the affine blow-ups - Cites Tag 01LH
  • Chapter 2: Schemes, Section 2.2.2: Gluing the affine blow-ups, Definition 2.2.2.2 - Cites Tag 01OF
  • Chapter 2: Schemes, Section 2.2.3: The universal property - Cites Tag 0806
  • Chapter 2: Schemes, Section 2.2.3: The universal property - Cites Tag 0805
  • Chapter 2: Schemes, Section 2.2.3: The universal property, Definition 2.2.3.1 - Cites Tag 0806
  • Chapter 2: Schemes, Section 2.2.3: The universal property, Definition 2.2.3.1 - Cites Tag 0805
  • Chapter 2: Schemes, Section 2.2.4: Transforms along a blow-up, Definition 2.2.4.1 - Cites Tag 080D
  • Chapter 2: Schemes, Section 2.2.6: Example: resolving the cusp - Cites Tag 080E
  • Chapter 2: Schemes, Section 2.1.1: Algebraic k-schemes, Definition 2.1.1.1 - Cites Tag 01T0
  • Chapter 2: Schemes, Section 2.1.4: Invertible ideal sheaves, Definition 2.1.4.1 - Cites Tag 01WS
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Theorem 4.2.6.3 - Cites Tag 020I
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Theorem 4.2.6.3 - Cites Tag 01VB
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Theorem 4.2.6.3 - Cites Tag 02VL
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Theorem 4.2.6.3 - Cites Tag 033B
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Theorem 4.2.6.3 - Cites Tag 02K5
  • Chapter 4: Main theorems, Section 4.2.6: Functorial resolution, Proof for Theorem 4.2.6.3 - Cites Tag 080B
  • Chapter 4: Main theorems, Section 4.2.7: Strong resolution of a variety, Theorem 4.2.7.1 - Cites Tag 01W8
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Definition 4.1.1.1 - Cites Tag 01WR
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Definition 4.1.1.1 - Cites Tag 01WS
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Definition 4.1.1.2 - Cites Tag 0806
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Definition 4.1.1.2 - Cites Tag 0806
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Theorem 4.1.1.3 - Cites Tag 00TV
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Theorem 4.1.1.3 - Cites Tag 00TV
  • Chapter 4: Main theorems, Section 4.1.1: Resolution of a variety, Proof for Theorem 4.1.1.3 - Cites Tag 00TV
• [Wat09] Sumio Watanabe. Algebraic Geometry and Statistical Learning Theory. Volume 25 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 2009. doi:10.1017/CBO9780511800474.
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  • Chapter 4: Main theorems, Section 4.1.2: Local monomialization of a real-analytic function, Theorem 4.1.2.2 - Cites Theorem 2.3
• [Wlo05] Jarosław Włodarczyk. Simple Hironaka resolution in characteristic zero. Journal of the American Mathematical Society, 18:779–822, 2005. doi:10.1090/S0894-0347-05-00493-5, arXiv:math/0401401.
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  • Chapter 1: Introduction, Section 1.3: Functorial resolution - Cites Theorem 1.0.2
  • Chapter 2: Schemes, Section 2.4.1: Finite successions of blow-ups, Definition 2.4.1.2 - Cites Theorem 1.0.2 (b)
  • Chapter 4: Main theorems, Section 4.2.4: Functorial principalization, Theorem 4.2.4.6 - Cites Section 3, Step 2
  • Chapter 4: Main theorems, Section 4.2.10: Embedded desingularization with smooth centres, Definition 4.2.10.3 - Cites Theorem 1.0.2 (d)
  • Chapter 4: Main theorems, Section 4.2.10: Embedded desingularization with smooth centres, Theorem 4.2.10.4 - Cites Theorem 4.7.1
  • Chapter 4: Main theorems, Section 4.2.10: Embedded desingularization with smooth centres, Proof for Theorem 4.2.10.4 - Cites §4.6–4.7
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites Theorem 4.7.1
• [Wlo09] Jarosław Włodarczyk. Resolution of singularities of analytic spaces. In Proceedings of the 15th Gökova Geometry–Topology Conference (2008), 31–63. International Press, 2009. URL: https://gokovagt.org/proceedings/2008/ggt08-wlodarczyk.pdf.
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  • Document root
  • Chapter 3: Analytic geometry, Section 3.1.3: Ideal sheaves, Definition 3.1.3.3 - Cites Theorem 2.0.2 (2)
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.1 - Cites Definition 3.2.4 (2)
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.1 - Cites Theorem 2.0.3 (2)
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.2 - Cites Theorem 2.0.2 (3)
  • Chapter 3: Analytic geometry, Section 3.1.5: Simple normal crossings boundaries, Definition 3.1.5.2 - Cites Theorem 2.0.2 (6)
  • Chapter 3: Analytic geometry, Section 3.2.1: Finite successions of monoidal transformations, Definition 3.2.1.1 - Cites Theorem 2.0.3 (1)
  • Chapter 3: Analytic geometry, Section 3.2.1: Finite successions of monoidal transformations, Definition 3.2.1.1 - Cites Definitions 3.2.5, 3.2.6
  • Chapter 3: Analytic geometry, Section 3.2.2: Restriction, extension and compatible families, Definition 3.2.2.1 - Cites Definition 3.2.6
  • Chapter 3: Analytic geometry, Section 3.2.4: Pull-back along a local analytic isomorphism, Definition 3.2.4.1 - Cites Theorem 3.5.1 (2)
  • Chapter 3: Analytic geometry, Section 3.2.4: Pull-back along a local analytic isomorphism, Definition 3.2.4.1 - Cites Proposition 3.4.1; Definition 3.4.2
  • Chapter 3: Analytic geometry, Section 3.2.4: Pull-back along a local analytic isomorphism, Definition 3.2.4.1 - Cites Definition 3.2.6
  • Chapter 3: Analytic geometry, Section 3.2.4: Pull-back along a local analytic isomorphism, Definition 3.2.4.1 - Cites Proposition 3.4.1 (1)
  • Chapter 1: Introduction, Section 1.3: Functorial resolution - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3: Analytic manifolds and analytic spaces - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Definition 4.3.1.1 - Cites Theorem 2.0.3 (2)
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Theorem 4.3.1.2 - Cites Definition 3.2.4
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Theorem 4.3.1.2 - Cites Theorem 2.0.3 (4)
  • Chapter 4: Main theorems, Section 4.3.1: Main Theorem II″(N), compatible-family form, Theorem 4.3.1.2 - Cites Theorem 2.0.3 (2)
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Theorem 2.0.3 (2)
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.2: Real-analytic principalization with the Jacobian condition, Theorem 4.3.2.1 - Cites Lemma 4.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.1 - Cites Theorem 2.0.3 (1)–(3); Lemma 4.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.1 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.1 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.2 - Cites Theorem 3.5.1
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.4 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.4 - Cites Remark (3) after Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.4 - Cites Theorem 3.5.1 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Theorem 3.5.1 (2)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Theorem 2.0.1 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Theorem 3.5.1 (2)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Theorem 2.0.1 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Proposition 3.4.1
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.5 - Cites Theorem 3.5.1 (1)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.6 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Definition 4.3.3.6 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Remark (3) after Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 3.5.1 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 3.5.1 (2)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 2.0.1 (3)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 3.5.1 (1)
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.3: Functorial principalization on analytic manifolds, Theorem 4.3.3.7 - Cites Lemma 4.0.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.1 - Cites Theorem 2.0.2 (1)–(3), (6)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.2 - Cites Theorem 2.0.2
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.2 - Cites Theorem 2.0.2
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.2 - Cites Lemma 4.0.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.4 - Cites Theorem 2.0.2 (4)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.4 - Cites Theorem 3.5.1 (2)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.4 - Cites Theorem 2.0.2 (4)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.4 - Cites Theorem 3.5.1 (2)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.4 - Cites Theorem 3.5.1 (1)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.5 - Cites Theorem 2.0.2 (4)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.5 - Cites Theorem 2.0.2 (4)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Definition 4.3.4.5 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites Definition 3.2.6
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites Lemma 4.0.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites Remark (2) after Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites Theorem 3.5.1 (1)
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites Theorem 2.0.3
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Theorem 4.3.4.6 - Cites Remark after Lemma 5.3.7
  • Chapter 4: Main theorems, Section 4.3.4: Embedded desingularization of analytic spaces, Proof for Theorem 4.3.4.6 - Cites Theorem 7.4.1
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.1 - Cites Theorem 2.0.1
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.2 - Cites Theorem 2.0.2
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.3 - Cites Theorem 2.0.1 (3)
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Definition 4.3.5.3 - Cites Theorem 2.0.1
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Theorem 4.3.5.5 - Cites Theorem 2.0.1 (3)
  • Chapter 4: Main theorems, Section 4.3.5: Resolution of analytic spaces, Theorem 4.3.5.5 - Cites Theorem 2.0.2, (∗)
  • Chapter 4: Main theorems, Section 4.3.6: Resolution of a reduced complex-analytic space, Theorem 4.3.6.1 - Cites Theorem 2.0.1 (1)–(2)