3. Analytic geometry🔗

The objects and operations in terms of which the analytic theorems are stated: analytic manifolds with their ideal sheaves, submanifolds and blow-ups; finite successions, the compatible families over the compact subsets of a manifold and the pull-back of a succession along a local analytic isomorphism; and analytic spaces.

1. 3.1. Ideal sheaves, submanifolds and blow-ups
   1. 3.1.1. Analytic manifolds and maps
   2. 3.1.2. The sheaf of analytic functions and germs
   3. 3.1.3. Ideal sheaves
   4. 3.1.4. Closed submanifolds and blow-ups
   5. 3.1.5. Simple normal crossings boundaries
   6. 3.1.6. The Jacobian ideal and analytic isomorphisms
2. 3.2. Finite successions, compatible families and pull-backs
   1. 3.2.1. Finite successions of monoidal transformations
   2. 3.2.2. Restriction, extension and compatible families
   3. 3.2.3. Morphisms of successions
   4. 3.2.4. Pull-back along a local analytic isomorphism
   5. 3.2.5. Push-forward along a closed embedding
3. 3.3. Analytic spaces
   1. 3.3.1. K-local-ringed spaces
   2. 3.3.2. Local models and quotients
   3. 3.3.3. Analytic spaces and their morphisms
   4. 3.3.4. Resolution assignments