概型的几何（英文版）

图书标准信息

• 作者 [美]艾森邦德 著
• 出版社 世界图书出版公司
• 出版时间 2010-01
• 版次 1
• ISBN 9787510004742
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 294页
• 正文语种 英语

【内容简介】

　　概型理论是代数几何的基础，在代数几何的经典领域不变理论和曲线模中有了较好的发展。将代数数论和代数几何有机的结合起来，实现了早期数论学者们的愿望。这种结合使得数论中的一些主要猜测得以证明。
　　《概型的几何(英文版)》旨在建立起经典代数几何基本教程和概型理论之间的桥梁。例子讲解详实，努力挖掘定义背后的深层次东西。练习加深读者对内容的理解。学习《概型的几何(英文版)》的起点低，了解交换代数和代数变量的基本知识即可。《概型的几何(英文版)》揭示了概型和其他几何观点，如流形理论的联系。了解这些观点对学习《概型的几何(英文版)》是相当有益的，虽然不是必要。目次：基本定义；例子；射影概型；经典结构；局部结构；概型和函子。

【目录】

IBasicDefinitions
I.1AffineSchemes
I.1.1SchemesasSets
I.1.2SchemesasTopologicalSpaces
I.1.3AnInterludeonSheafTheoryReferencesfortheTheoryofSheaves
I.1.4SchemesasSchemes(StructureSheaves)
I.2SchemesinGeneral
I.2.1Subschemes
I.2.2TheLocalRingataPoint
I.2.3Morphisms
I.2.4TheGluingConstructionProjectiveSpace
I.3RelativeSchemes
I.3.1FiberedProducts
I.3.2TheCategoryofS-Schemes
I.3.3GlobalSpec
I.4TheFunctorofPoints

IIExamples
II.1ReducedSchemesoverAlgebraicallyClosedFields
II.1.1AffineSpaces
II.1.2LocalSchemes
II.2ReducedSchemesoverNon-AlgebraicallyClosedFields
II.3NonreducedSchemes
II.3.1DoublePoints
II.3.2MultiplePointsDegreeandMultiplicity
II.3.3EmbeddedPointsPrimaryDecomposition
II.3.4FlatFamiliesofSchemes
Limits
Examples
Flatness
II.3.5MultipleLines
II.4ArithmeticSchemes
II.4.1SpecZ
II.4.2SpecoftheRingofIntegersinaNumberField
II.4.3AffineSpacesoverSpecZ
II.4.4AConicoverSpecZ
II.4.5DoublePointsinAl

IIIProjectiveSchemes
III.1AttributesofMorphisms
III.1.1FinitenessConditions
III.1.2PropernessandSeparation
III.2ProjofaGradedRing
III.2.1TheConstructionofProjS
III.2.2ClosedSubschemesofProjR
III.2.3GlobalProj
ProjofaSheafofGraded0x-Algebras
TheProjectivizationP(ε)ofaCoherentSheafε
III.2.4TangentSpacesandTangentCones
AffineandProjectiveTangentSpaces
TangentCones
III.2.5MorphismstoProjectiveSpace
III.2.6GradedModulesandSheaves
III.2.7Grassmannians
III.2.8UniversalHypersurfaces
III.3InvariantsofProjectiveSchemes
III.3.1HilbertFunctionsandHilbertPolynomials
1II.3.2FlatnessIl：FamiliesofProjectiveSchemes
III.3.3FreeResolutions
III.3.4Examples
PointsinthePlane
Examples：DoubleLinesinGeneralandinp3
III.3.5BEzoutsTheorem
MultiplicityofIntersections
III.3.6HilbertSeries

IVClassicalConstructions
IV.1FlexesofPlaneCurves
IV.I.1Definitions
IV.1.2FlexesonSingularCurves
IV.1.3CurveswithMultipleComponents
IV.2Blow-ups
IV.2.1DefinitionsandConstructions
AnExample：BlowingupthePlane
DefinitionofBlow-upsinGeneral
TheBlowupasProj
Blow-upsalongRegularSubschemes
IV.2.2SomeClassicBlow-Ups
IV.2.3Blow-upsalongNonreducedSchemes
BlowingUpaDoublePoint
BlowingUpMultiplePoints
Thej-Function
IV.2.4Blow-upsofArithmeticSchemes
IV.2.5Project：QuadricandCubicSurfacesasBlow-ups
IV.3Fanoschemes
IV.3.1Definitions
IV.3.2LinesonQuadrics
LinesonaSmoothQuadricoveranAlgebraically
ClosedField
LinesonaQuadricCone
AQuadricDegeneratingtoTwoPlanes
MoreExamples
IV.3.3LinesonCubicSurfaces
IV.4Forms

VLocalConstructions
V.1Images
V.I.1TheImageofaMorphismofSchemes
V.1.2UniversalFormulas
V.1.3FittingIdealsandFittingImages
FittingIdeals
FittingImages
V.2Resultants
V.2：lDefinitionoftheResultant
V.2.2SylvestersDeterminant
V.3SingularSchemesandDiscriminants
V.3.1Definitions
V.3.2Discriminants
V.3.3Examples
V.4DualCurves
V.4.1Definitions
V.4.2DualsofSingularCurves
V.4.3CurveswithMultipleComponents
V.5DoublePointLoci

VISchemesandFunctors
VI.1TheFunctorofPoints
VI.I.1OpenandClosedSubfunctors
VI.1.2K-RationalPoints
VI.1.3TangentSpacestoaFunctor
VI.1.4GroupSchemes
VI.2CharacterizationofaSpacebyits~nctorofPoints
VI.2.1CharacterizationofSchemesamongFunctors
VI.2.2ParameterSpaces
TheHilbertScheme
ExamplesofHilbertSchemes
VariationsontheHilbertSchemeConstruction.
VI.2.3TangentSpacestoSchemesinTermsofTheirFunc
torsofPoints
TangentSpacestoHilbertSchemes
TangentSpacestoFanoSchemes
VI.2.4ModuliSpaces
References
Index