代数几何-复代数簇.代数曲线及雅可比行列式-III-44-(影印版) 本书特色

The first contributioof this EMS volume ocomplex algebraic geometry touchres upomany ofthe central problems ithis vast and very active area of current research. While it is much too short to
　　provide complete coverage of this subject， it provides a succinct summary of the areas it covers， while providing in-depth coverage ofcertaivery important fields.
　　The second part provides a l，rief and lucid introductioto the recent work othe interactions betweethe classical area of the geometry ofcomplex algebraic curves and their Jacobiavarieties， and Partial differential Equations ofmathematical physics. The paper discusses the work of Mumford， Novikov， Krichever， and Shiots， and would be aexcellent companioto the older classics othe subject.

代数几何-复代数簇.代数曲线及雅可比行列式-III-44-(影印版) 内容简介

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代数几何-复代数簇.代数曲线及雅可比行列式-III-44-(影印版) 目录

Introduction

Chapter 1． Classical Hodge Theory
1．Algebraic Varieties
2．Complex Manifolds
3．A ComparisoBetweeAlgebraic Varieties and Analytic Spaces
4．Complex Manifolds as C Manifolds
5．Connections oHolomorphic Vector Bundles
6．HermitiaManifolds
7．Kahler Manifolds
8．Line Bundles and Divisors
9．The Kodaira Vanishing Theorem
10．Monodromy

Chapter 2． Periods of Integrals oAlgebraic Varieties
1．Classifying Space
2．Complex Tori
3．The Period Mapping
4．Variatioof Hodge Structures
5．Torelli Theorems
6．Infinitesimal Variatioof Hodge Structures

Chapter 3． Torelli Theorems
1．Algebraic Curves
2．The Cubic Threefold
3．K3 Surfaces and Elliptic Pencils
4．Hypersurfaces
5．Counterexamples to Torelli Theorems

Chapter 4． Mixed Hodge Structures
1．Definitioof mixed Hodge structures
2．Mixed Hodge structure othe Cohomology of a Complete Variety with Normal Crossings
3．Cohomology of Smooth Var/eties
4．The Invariant Subspace Theorem
5．Hodge Structure othe Cohomology of Smooth Hypersurfaces
6．Further Development of the Theory of Mixed Hodge Structures

Chapter 5．Degenerations of Algebraic Varieties
1．Degenerations of Manifolds
2．The Limit Hodge Structure
3．The Clemens-Schmid Exact Sequence
4．AApplicatioof the Clemens-Schmid Exact Sequence to theDegeneratioof Curves
5．AApplicatioof the Clemens-Schmid Exact Sequence to Surface Degenerations The Relationship Betweethe Numerical Invariants of the Fibers Xt and Xo
6．The Epimorphicity of the Period Mapping for K3 Surfaces

Comments othe bibliography
References
Index

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