Calabi-Yau流形和相关几何

Preface

Part 1 Riemannian Holonomy Groups and Calibrated Geometry

1 Introduction

2 Introduction to Holonomy Groups

3 Berger's Classification of Holonomy Groups

4 Kahler Geometry and Holonomy

5 The Calabi Conjecture

6 The Exceptional Holonomy Groups

7 Introduction to Calibrated Geometry

8 Calibrated Submanifolds in Rn

9 Constructions of SL m-folds in Cm

10 Compact Calibrated Submanifolds

11 Singularities of Special Lagrangian m-folds

12 The SYZ Conjecture, and SL Fibrations

Part 2 Calabi-Yau Manifolds and Mirror Symmetry

13 Introduction

14 The Classical Geometry of Calabi-Yau Manifolds

15 Kahler Moduli and Gromov-Witten Invariants

16 Variation and Degeneration of Hodge Structures

17 A Mirror Conjecture

18 Mirror Symmetry in Practice

19 The Strominger-Yau-Zaslow Approach to Mirror Symmetry

Part 3 Compact Hyperkahler Manifolds

20 Introduction

21 Holomorphic Symplectlc Manifolds

22 Deformations of Complex Structures

23 The Beauville-Bogomolov Form

24 Cohomology of Compact Hyperkahler Manifolds

25 Twistor Space and Moduli Space

26 Projectivity of Hyperkahler Manifolds

27 Birational Hyperkahler Manifolds

28 The （Birational） Kahler Cone

References

Index

Each summer since 1996, algebraic geometers and algebraists in Norway have organised a summer school in Nordfjordeid, a small place in the western part of Norway. In addition to the beauty of the place, located between the mountains, close to the fjord and not far from the Norway's largest glacier,a reason for going there is that Sophus Lie was born and spent his few first years in Nordfjordeid, so it has a flavour of both the exotic and pilgrimage.It is also convenient: the municipality of Eid has created a conference centre named after Sophus Lie, aimed at attracting activities to fill the summer term of the local boarding school.