代数几何中的解析方法 英文版PDF|Epub|txt|kindle电子书版本网盘下载

代数几何中的解析方法 英文版PDF格式电子书版下载

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Introduction1

Chapter 1． Preliminary Material:Cohomology,Currents5

1.A. Dolbeault Cohomology and Sheaf Cohomology5

1.B. Plurisubharmonic Functions6

1.C. Positive Currents9

Chapter 2．Lelong numbers and Intersection Theory15

2.A. Multiplication of Currents and Monge-Ampère Operators15

2.B. Lelong Numbers18

Chapter 3．Hermitian Vector Bundles, Connections and Curvature.25

Chapter 4．Bochner Technique and Vanishing Theorems31

4.A. Laplace-Beltrami Operators and Hodge Theory31

4.B. Serre Duality Theorem32

4.C. Bochner-Kodaira-Nakano Identity on K？hler Manifolds33

4.D. Vanishing Theorems34

Chapter 5．L2 Estimates and Existence Theorems37

5.A. Basic L2 Existence Theorems37

5.B. Multiplier Ideal Sheaves and Nadel Vanishing Theorem39

Chapter 6．Numerically Effective and Pseudo-effective Line Bundles47

6.A. Pseudo-effective Line Bundles and Metrics with Minimal Singularities47

6.B. Nef Line Bundles49

6.C. Description of the Positive Cones51

6.D. The Kawamata-Viehweg Vanishing Theorem56

6.E. A Uniform Global Generation Property due to Y.T. Siu58

Chapter 7．A Simple Algebraic Approach to Fujita's Conjecture61

Chapter 8．Holomorphic Morse Inequalities71

8.A. General Analytic Statement on Compact Complex Manifolds71

8.B. Algebraic Counterparts of the Holomorphic Morse Inequalities72

8.C. Asymptotic Cohomology Groups74

8.D. Transcendental Asymptotic Cohomology Functions78

Chapter 9．Effective Version of Matsusaka's Big Theorem83

Chapter 10．Positivity Concepts for Vector Bundles89

Chapter 11．Skoda's L2 Estimates for Surjective Bundle Morphisms99

11.A. Surjectivity and Division Theorems99

11.B. Applications to Local Algebra: the Brian？on-Skoda Theorem105

Chapter 12．The Ohsawa-Takegoshi L2 Extension Theorem111

12.A. The Basic a Priori Inequality111

12.B. Abstract L2 Existence Theorem for Solutions of ？-Equations112

12.C. The L2 Extension Theorem114

12.D. Skoda's Division Theorem for Ideals of Holomorphic Functions122

Chapter 13．Approximation of Closed Positive Currents by Analytic Cycles127

13.A. Approximation of Plurisubharmonic Functions Via Bergman Kernels127

13.B. Global Approximation of Closed(1,1)-currents on a Compact Complex Manifold129

13.C. Global Approximation by Divisors136

13.D. Singularity Exponents and log Canonical Thresholds143

13.E. Hodge Conjecture and approximation of(p,p)- currents148

Chapter 14．Subadditivity of Multiplier Ideals and Fujita's Approximate Zariski Decomposition153

Chapter 15．Hard Lefschetz Theorem with Multiplier Ideal Sheaves159

15.A. A Bundle Valued Hard Lefschetz Theorem159

15.B. Equisingular Approximations of Quasi Plurisubharmonic Functions160

15.C. A Bochner Type Inequality166

15.D. Proof of Theorem 15.1168

15.E. A Counterexample170

Chapter 16．Invariance of Plurigenera of Projective Varieties173

Chapter 17．Numerical Characterization of the K？hler Cone177

17.A. Positive Classes in Intermediate(p,p)-bidegrees177

17.B. Numerically Positive Classes of Type(1,1)178

17.C. Deformations of Compact K？hler Manifolds184

Chapter 18．Structure of the Pseudo-effective Cone and Mobile Intersection Theory189

18.A. Classes of Mobile Curves and of Mobile(n-1,n-1)-currents189

18.B. Zariski Decomposition and Mobile Intersections192

18.C. The Orthogonality Estimate199

18.D. Dual of the Pseudo-effective Cone202

18.E. A Volume Formula for Algebraic(1,1)-classes on Projective Surfaces205

Chapter 19．Super-canonical Metrics and Abundance209

19.A. Construction of Super-canonical Metrics209

19.B. Invariance of Plurigenera and Positivity of Curvature of Super-canonical Metrics216

19.C. Tsuji's Strategy for Studying Abundance217

Chapter 20．Siu's Analytic Approach and P？un's Non Vanishing Theorem219

References223