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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