作者：(俄罗斯)帕尔申(Parshin)等
页数：270
出版社：科学出版社
出版日期：2009
ISBN：9787030234872
电子书格式：pdf/epub/txt
内容简介
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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.
目录
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
