Classification of Higher Dimensional Algebraic Varieties

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Springer Science & Business Media, May 27, 2010 - Mathematics - 220 pages
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Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.

 

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Contents

CHAPTER 1 Introduction
3
CHAPTER 2 Preliminaries
17
CHAPTER 3 Singularities
27
Part II Recent advances in the minimal model program
46
CHAPTER 4 Introduction
49
CHAPTER 5 The main result
51
CHAPTER 6 Multiplier ideal sheaves
67
CHAPTER 7 Finite generation of the restricted algebra
79
Part III Compact moduli spaces of canonically polarized varieties
103
CHAPTER 11 Moduli problems
105
CHAPTER 12 Hilbert schemes
111
CHAPTER 13 The construction of the moduli space
116
CHAPTER 14 Families and moduli functors
133
CHAPTER 15 Singularities of stable varieties
141
CHAPTER 16 Subvarieties of moduli spaces
148
Part IV Solutions and hints to some of the exercises
172

CHAPTER 8 Log terminal models
82
CHAPTER 9 Nonvanishing
89
CHAPTER 10 Finiteness of log terminal models
98
Bibliography
185
Index
203
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