Desingularization: Invariants and Strategy

Chapter 1 Introduction

Chapter 2 Basic Invariants for Singularities

Chapter 3 Permissible Blow-Ups

Chapter 4 ℬ $$\mathcal {B}$$ -Permissible Blow-Ups: The Embedded Case

Chapter 5 ℬ $$ \mathcal {B}$$ -Permissible Blow-Ups: The Non-embedded Case

Chapter 6 Main Theorems and Strategy for Their Proofs

Chapter 7 ( u )-standard Bases

Chapter 8 Characteristic Polyhedra of J  ⊂  R

Chapter 9 Transformation of Standard Bases Under Blow-Ups

Chapter 10 Termination of the Fundamental Sequences of ℬ $$ \mathcal {B}$$ -Permissible Blow-Ups, and the Case e x ( X ) = 1

Chapter 11 Additional Invariants in the Case e x ( X ) = 2

Chapter 12 Proof in the Case e x ( X ) =  es x ( X ) = 2 , I: Some Key Lemmas

Chapter 13 Proof in the Case e x ( X ) = e ¯ x ( X ) = 2 $$e_x(X)=\overline {e}_x(X)=2$$ , II: Separable Residue Extensions

Chapter 14 Proof in the Case e x ( X ) =  e x ( X ) = 2 , III: Inseparable Residue Extensions

Chapter 15 Non-existence of Maximal Contact in Dimension 2

Chapter 16 An Alternative Proof of Theorem 6.17

Chapter 17 Functoriality, Locally Noetherian Schemes, Algebraic Spaces and Stacks

Chapter 18 Appendix. Hironaka’s Characteristic Polyhedron. Notes for Novices(B.Schober)