国外数学名著系列（续1）（影印版）44：代数几何3（复代数簇，代数曲线及雅可比行列式）

图书标准信息

• 作者 [俄罗斯]帕尔申 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030234872
• 定价 66.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 270页
• 字数 340千字
• 正文语种 英语
• 丛书 国外数学名著系列44

【内容简介】

《国外数学名著系列（续1）（影印版）44：代数几何3（复代数簇，代数曲线及雅可比行列式）》discussesthe.workofMumford，Novikov，Krichever，andShiota，andwouldbeanexcellentcompaniontotheolderclassicsonthesubject.ThefirstcontributionofthisEMSvolumeoncomplexalgebraicgeometrytouchesuponmanyofthecentralproblemsinthisvastandveryactiveareaofcurrentresearch.Whileitismuchtooshorttoprovidecompletecoverageofthissubject，itprovidesasuccinctsummaryoftheareasitcovers，whileprovidingin-depthcoverageofcertainveryimportantfields.ThesecondpartprovidesabriefandlucidintroductiontotherecentworkontheinteractionsbetweentheclassicalareaofthegeometryofcomplexalgebraiccurvesandtheirJacobianvarieties，andpartialdifferentialequationsofmathematicalphysics.

【目录】

Introduction
Chapter1.ClassicalHodgeTheory
1.AlgebraicVarieties
2.ComplexManifolds
3.AComparisonBetweenAlgebraicVarietiesandAnalyticSpaces
4.ComplexManifoldsasCManifolds
5.ConnectionsonHolomorphicVectorBundles
6.HermitianManifolds
7.KahlerManifolds
8.LineBundlesandDivisors
9.TheKodairaVanishingTheorem
10.Monodromy

Chapter2.PeriodsofIntegralsonAlgebraicVarieties
1.ClassifyingSpace
2.ComplexTori
3.ThePeriodMapping
4.VariationofHodgeStructures
5.TorelliTheorems
6.InfinitesimalVariationofHodgeStructures

Chapter3.TorelliTheorems
1.AlgebraicCurves
2.TheCubicThreefold
3.K3SurfacesandEllipticPencils
4.Hypersurfaces
5.CounterexamplestoTorelliTheorems

Chapter4.MixedHodgeStructures
1.DefinitionofmixedHodgestructures
2.MixedHodgestructureontheCohomologyofaCompleteVarietywithNormalCrossings
3.CohomologyofSmoothVarieties
4.TheInvariantSubspaceTheorem
5.HodgeStructureontheCohomologyofSmoothHypersurfaces
6.FurtherDevelopmentoftheTheoryofMixedHodgeStructures

Chapter5.DegenerationsofAlgebraicVarieties
1.DegenerationsofManifolds
2.TheLimitHodgeStructure
3.TheClemens-SchmidExactSequence
4.AnApplicationoftheClemens-SchmidExactSequencetotheDegenerationofCurves
5.AnApplicationoftheClemens-SchmidExactSequenceto
SurfaceDegenerations.TheRelationshipBetweentheNumerical
InvariantsoftheFibersXtandX0
6.TheEpimorphicityofthePeriodMappingforK3Surfaces
Commentsonthebibliography
References
Index