紧复曲面 原书第2版PDF电子书下载

Introduction 1

Historical Note 1

The Contents of the Book 8

Standard Notation 12

Ⅰ.Preliminaries 13

Topology and Algebra 13

1. Notation and Basic Facts 13

2. Some Properties of Bilinear Forms 15

3. Vector Bundles, Characteristic Classes and the Index Theorem 21

Complex Manifolds 23

4. Basic Concepts and Facts 23

5. Holomorphic Vector Bundles, Serre Duality and Riemann-Roch 24

6. Line Bundles and Divisors 26

7. Algebraic Dimension and Kodaira Dimension 28

General Analytic Geometry 30

8. Complex Spaces 30

9. The σ-Process 34

10. Deformations of Complex Manifolds 35

Differential Geometry of Complex Manifolds 39

11. De Rham Cohomology 39

12. Dolbeault Cohomology 41

13. Kanler Manifolds 42

14. Weight-1 Hodge Structures 48

15. Yaus results on Kahler-Einstein Metrics 51

Coverings 53

16. Ramification 53

17. Cyclic Coverings 54

18. Covering Tricks 55

Projective-Algebraic Varieties 57

19. GAGA Theorems and Proiectivitv Criteria 57

20. Tneorems of ertmi and Letscnetz 58

Ⅱ.Curves on Surfaces 61

Embedded Curves 61

1. Some Standard Exact Sequences 61

2. The Picard-Group of an Embedded Curve 63

3. Riemann-Roch for an Embedded Curve 65

4. The Residue Theorem 66

5. The Trace Map 68

6. Serre Duality on an Embedded Curve 70

7. The σ-process 75

8. Simple Singularities of Curves 78

Intersection Theory 81

9. Intersection Multiplicities 81

10. Intersection Numbers 83

11. The Arithmetical Genus of an Embedded Curve 84

12. 1-Connected Divisors 85

Ⅲ.Mappings of Surfaces 89

Bimeromorphic Geometry 89

1. Bimeromorphic Maps 89

2. Exceptional Curves 90

3. Rational Singularities 93

4. Exceptional Curves of the First Kind 97

5. Hirzebruch-Jung Singularities 99

6. Resoiution or Surface Singuiarities 105

7. Singularities of Double Coverings, Simple Singularities of Surfaces 107

Fibrations of Surfaces 110

8. Generalities on Fibrations 110

9. The n-th Root Fibration 113

10. Stable Fibrations 114

11. Direct Image Sheaves 116

12. Relative Duality 118

The Period Map of Stable Fibrations 121

13. Period Matrices of Stable Curves 121

14. Topological Monodromy of Stable Fibrations 122

15. Monodromy of the Period Matrix 125

16. Extending the Period Map 127

17. The Degree of fωx/s 129

18. Iitaka's Conjecture C2,1 131

Ⅳ.Some General Properties of Surfaces 135

1. Meromorphic Maps, Associated to Line Bundles 135

2. Hodge Theory on Surfaces 137

3. Existence of K？hler Metrics 144

4. Deformations of Surfaces 154

5. Some Inequalities for Hodge Numbers 157

6. Projectivity of Surfaces 159

7. The Nef Cone 162

8. Surfaces of Algebraic Dimension Zero 165

9. Almost-Complex Surfaces without any Complex Structure 166

10. Bogomolov's Theorem 168

11. Reider's Method 174

12. Vanishing Theorems on Surfaces 179

Ⅴ.Examples 185

Some Classical Examples 185

1. The Projective Plane P2 185

2. Complete Intersections 187

3. Tori of Dimension 2 188

Fibre Bundles 189

4. Ruled Surfaces 189

5. Elliptic Fibre Bundles 193

6. Higher Genus Fibre Bundles 199

Elliptic Fibrations 200

7. Kodaira's Table of Singular Fibres 200

8. Stable Fibrations 202

9. The Jacobian Fibration 204

10. Stable Reduction 207

11. Classification 211

12. Invariants 212

13. Logarithmic Transformations 216

Kodaira Fibrations 220

14. Kodaira Fibrations 220

Finite Quotients 223

15. The Godeaux Surface 223

16. Kummer Surfaces 224

17. Quotients of Products of Curves 224

Infinite Quotients 225

18. Hopf Surfaces 225

19. Inoue Surfaces 227

20. Quotients of Bounded Domains in C2 230

21. Hilbert Modular Surfaces 231

Coverings 236

22. Invariants of Double Coverings 236

23. An Enriques Surface 238

24. Kummer Coverings 240

Ⅵ.The Enriques Kodaira Classification 243

1. Statement of the Main Result 243

2. Characterising Minimal Surfaces whose Canonical Bundle is Nef 247

3. The Rationality Theorem and Castelnuovo's Criterion 248

4. The Case a（X）＝2 252

5. The Case a（X）＝1 255

6. The Case a（X）＝0 257

7. The Final Step 262

8. Deformations 263

Ⅶ.Surfaces of General Type 269

Preliminaries 269

1. Introduction 269

2. Some General Theorems 271

Two Inequalities 273

3. Noether's Inequality 273

4. The Inequalityc21≤3c2 275

Pluricanonical Maps 279

5. The Main Results 279

6. Proof of the Main Results 281

7. The Exceptional Cases and the 1-Canonical Map 286

Surfaces with Given Chern Numbers 290

8. The Geography of Chern Numbers 291

9. Surfaces on the Noether Lines 296

10. Surfaces with q＝pg＝0 299

Ⅷ.K3-Surfaces and Enriques Surfaces 307

Introduction 307

1. Notation 307

2. The Results 309

K 3-Surfaces 310

3. Topological and Analvtical Invariants 310

4. Digression on Affne Geometrv over F2 314

5. ne Neron-Severi Lattice of Kummer Surfaces 316

6. The Torelli Theorem for Kummer Surfaces 322

7. The Local Torelli Theorem for K3-Surfaces 323

8. A Density Theorem 325

9. Behaviour of the K？hler Cone under Deformations 327

10. Degenerations of Isomorphisms between K3-Surfaces 329

11. The Torelli T neorems for K3-Surfaces 332

12. Construction of Moduli Spaces 334

13. Digression on Quaternionic Structures 336

14. Surjectivity of the Period Map 338

Enriques Surfaces 339

15. Topological and Analytic Invariants 339

16. Divisors on an Enriques Surface Y 340

17. Elliptic Pencils 342

18. Double Coverings of Quadrics 345

19. The Period Map 350

20. The Period Domain for Enriques Surfaces 352

21. Global Properties of the Period Map 354

Special Topics 358

22. Proiective K3-surfaces and Mirror Symmetry 358

23. Special Curves onK3-Surfaces 364

24. An Application to Hyperbolic Geometry 369

Ⅸ.Topological and Differentiable Structure of Surfaces 375

Topology of Simply Connected Compact Complex Surfaces 375

1. Freedman's Results 375

2. Representability of Unimodular Forms 377

Donaldson Invariants 379

3. Introduction 379

4. The Donaldson Invariant,a Bird's Eve View 380

5. Infiniteiy many Homeomorphic Surfaces which are not Ditteomorphic 383

6. FurtherResults obtained by the Donaldson Method 390

Seiberg-Witten Invariants 391

7. Introduction 391

8. Properties of the Invariants 393

9.Surfaces Diffeomorpnic to a Rational urface 395

Bibliography 401

Notation 425

Index 429