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Tables of Contents for Geometry Of Higher Dimensional Algebraic Varieties
Chapter/Section Title
Page #
Page Count
Preface
vi
Part I Geometry of Rational Curves on Varieties
3
128
Introduction: Why Rational Curves
3
3
Lecture I: Deformations and Rational Curves
6
22
Lecture II: Construction of Non-Trivial Deformations via Frobenius
28
24
Lecture III: Foliations and Purely Inseparable Coverings
52
23
Lecture IV: Abundance for Minimal 3-Folds
75
22
Lecture V: Rationally Connected Fibrations and Applications
97
34
References
121
10
Part II An Introduction to the Classification of Higherdimensional Complex Varieties
131
75
Preface
131
2
Prerequisites
133
73
N Notations
133
2
0 Surfaces and a first View to Higher Dimensions
135
2
1 Sigularities
137
8
2 Vanishing Theorems
145
7
3 The Ample Cone
152
3
4 The Base Point Free Theorem
155
10
5 The Cone Theorem
165
4
6 Fano Manifolds and the Structure of Contractions of Extremal Rays
169
9
7 Surfaces and Threefolds
178
8
8 Minimal Models
186
10
9 A View to Adjunction Theory
196
5
10 Calabi-Yau Threefolds
201
5
References
206
9
Index
215