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Contents
Preface vii
Chapter 1. Introduction 1
§1.1. Notation 2
Chapter 2. Non-singularity and Resolution of Singularities 3
§2.1. Newton's method for determining the branches of a plane
curve 3
§2.2. Smoothness and non-singularity 7
§2.3. Resolution of singularities 9
§2.4, Normalization 10
§2.5. Local uniformization and generalized resolution problems 11
Chapter 3. Curve Singularities 17
§3.1. Blowing up a point on
A2
17
§3.2. Completion 22
§3.3. Blowing up a point on a non-singular surface 25
§3.4. Resolution of curves embedded in a non-singular surface I 26
§3.5. Resolution of curves embedded in a non-singular surface II 29
Chapter 4. Resolution Type Theorems 37
§4.1. Blow-ups of ideals 37
§4.2. Resolution type theorems and corollaries 40
Chapter 5. Surface Singularities 45
§5.1. Resolution of surface singularities 45

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