Calabi-Yau流形和相关几何 英文PDF电子书下载

Part ⅠRiemannian Holonomy Groups and Calibrated Geometry&Dominic Joyce 3

1 Introduction 3

2 Introduction to Holonomy Groups 4

3 Berger's Classification of Holonomy Groups 10

4 K？hler Geometry and Holonomy 14

5 The Calabi Conjecture 20

6 The Exceptional Holonomy Groups 26

7 Introduction to Calibrated Geometry 31

8 Calibrated Submanifolds in IRn 36

9 Constructions of SL m-folds in Cm 41

10 Compact Calibrated Submanifolds 50

11 Singularities of Special Lagrangian m-folds 57

12 The SYZ Conjecture, and SL Fibrations 63

Part ⅡCalabi-Yau Manifolds and Mirror Symmetry&Mark Gross 71

13 Introduction 71

14 The Classical Geometry of Calabi-Yau Manifolds 72

15 K？hler Moduli and Gromov-Witten Invariants 93

16 Variation and Degeneration of Hodge Structures 102

17 A Mirror Conjecture 121

18 Mirror Symmetry in Practice 122

19 The Strominger-Yau-Zaslow Approach to Mirror Symmetry 140

Part ⅢCompact Hyperk？hler Manifolds&Daniel Huybrechts 163

20 Introduction 163

21 Holomorphic Symplectic Manifolds 164

22 Deformations of Complex Structures 172

23 The Beauville-Bogomolov Form 177

24 Cohomology of Compact Hyperk？hler Manifolds 190

25 Twistor Space and Moduli Space 196

26 Projectivity of Hyperk？hler Manifolds 203

27 Birational Hyperk？hler Manifolds 213

28 The（Birational） K？hler Cone 221

References 227

Index 237