代数几何中的解析方法
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作者(法)德马依 著
出版社高等教育出版社
ISBN9787040305319
出版时间2011-01
版次1
装帧精装
开本16开
纸张胶版纸
页数231页
字数99999千字
定价48元
上书时间2024-03-19
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基本信息
书名:代数几何中的解析方法
定价：48元
作者:(法)德马依 著
出版社：高等教育出版社
出版日期：2011-01-01
ISBN：9787040305319
字数：350000
页码：231
版次：1
装帧：精装
开本：16开
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IntroductionChapter 1. Preliminary Material: Cohomology, Currents1.A. Dolbeault Cohomology and Sheaf Cohomology1.B. Plurisuhharmonic Functio1.C. Positive CurrentsChapter 2. Lelong numbe and Inteection Theory2.A. Multiplication of Currents and Monge-Ampere Operato2.B. Lelong NumbeChapter 3. Hermitian Vector Bundles,Connectio and CurvatureChapter 4. Bochner Technique and Vanishing Theorems4.A. Laplace-Beltrami Operato and Hodge Theory4.B. Serre Duality Theorem4.CBochner-Kodaira-Nakano Identity on Kahler Manifolds4.D. Vanishing TheoremsChapter 5. L2 Estimates and Estence Theorems5.A. Basic L2 Estence Theorems5.B. Multiplier Ideal Sheaves and Nadel Vanishing TheoremChapter 6. Numerically Effective andPseudo-effective Line Bundles6.A. Pseudo-effective Line Bundles and Metrics with MinimalSingularities6.B. Nef Line Bundles6.C. Description of the Positive Cones6.D. The Kawamat~-Viehweg Vanishing Theorem6.E. A Uniform Global Generation Property due to Y.T. SiuChapter 7. A Simple Algebraic Approach to Fujita's ConjectureChapter 8. Holomorphic Moe Inequalities8.A. General Analytic Statement on Compact Complex Manifolds8.B. Algebraic Counterparts of the Holomorphic Moe Inequalities8.C. Asymptotic Cohomology Groups8.D. Tracendental Asymptotic Cohomology FunctioChapter 9. Effective Veion of Matsusaka's Big TheoremChapter 10. Positivity Concepts for Vector BundlesChapter 11. Skoda's L2 Estimates for Surjective Bundle Morphisms11.A. Surjectivity and Division Theorems11.B. Applicatio to Local Algebra: the Brianqon-Skoda TheoremChapter 12. The Ohsawa-Takegoshi L2 Exteion Theorem12.A. The Basic a Priori Inequality12.B. Abstract L2 Estence Theorem for Solutio of O-Equatio12.C. The L2 Exteion Theorem12.D. Skoda's Division Theorem for Ideals of Holomorphic FunctioChapter 13. Appromation of Closed Positive Currentsby Analytic Cycles13.A. Appromation of Plurisubharmonic Functio Via Bergman kernels13.B. Global Appromation of Closed (1,1)-Currents on a CompactComplex Manifold13.C. Global Appromation by Diviso13.D. Singularity Exponents and log Canonical Thresholds13.E. Hodge Conjecture and appromation of (p, p)- currentsChapter 14. Subadditivity of Multiplier Idealsand Fujita's Appromate Zariski DecompositionChapter 15. Hard Lefschetz Theoremwith Multiplier Ideal Sheaves15.A. A Bundle Valued Hard Lefschetz Theorem15.B. Equisingular Appromatio of Quasi Plurisubharmonic Functio15.C. A Bochner Type Inequality15.D. Proof of Theorem 15.115.E. A CounterexampleChapter 16. Invariance of Plurigenera of Projective VarietiesChapter 17. Numerical Characterization of the K~ihler Cone17.A. Positive Classes in Intermediate (p, p)-bidegrees17.B. Numerically Positive Classes of Type (1,1)17.C. Deformatio of Compact K~hler ManifoldsChapter 18. Structure of the Pseudo-effective Coneand Mobile Inteection Theory18.A. Classes of Mobile Curves and of Mobile (n- 1, n-1)-currents18.B. Zariski Decomposition and Mobile Inteectio18.C. The Orthogonality Estimate18.D. Dual of the Pseudo-effective Cone18.E. A Volume Formula for Algebraic (1,1)-Classes on ProjectiveSurfacesChapter 19. Super-canonical Metrics and Abundance19.A. Cotruction of Super-canonical Metrics19.B. Invariance of Plurigenera and Positivity of Curvature ofSuper-canonical Metrics19.C. Tsuji's Strategy for Studying AbundanceChapter 20. Siu's Analytic Approach and Paun'sNon Vanishing TheoremReferences
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