《代數曲線幾何（第1卷）》是2014-年世界圖書出版公司出版的著作，作者是[義大利] E，Arbarello。
基本介紹
- 中文名：《代數曲線幾何（第1卷）》
- 作者：[義大利]E，Arbarello
- 出版時間：2014年05月01日
- 出版社：世界圖書出版公司
- ISBN：9787510075902
內容簡介,目錄,
內容簡介
Inrecentyearstherehasbeenenormousactivityinthetheoryofalgebraiccurves．Manylong·standingproblemshavebeensolvedusingthegeneraltechniquesdevelopedinalgebraicgeometryduringthe1950’Sand1960’S．Additionally，unexpectedanddeepconnectionsbetweenalgebraiccurvesanddifferentialequationshavebeenuncovered．andtheseinturnshedlightonotherclassicalproblemsincurvetheory．Itseemsfairtosaythatthetheoryofalgebraiccurveslookscompletelyditierentnowfromhowitappeared15yearsago；inparticular，ourcurrentstateofknowledgerepre-sentsasignificantadvancebeyondthelegacyleftbytheclassicalgeometerssuchasNoether，Castelnuovo，Enriques，andSeveri．
Thesebooksgiveapresentationofoneofthecentralareasofthisrecentactivity：namely，thestudyoflinearseriesonbothafixedcurve（VolumeI）andonavariablecurverVolumeII ．OurgoaliStogiveacomprehensiveandself-containedaccountoftheextrinsicgeometryofalgebraiccurves，whichinouropinionconstitutesthemaingeometriccoreoftherecentadvancesincurvetheory．Alongthewayweshall，ofcourse，discussappli．cationsofthetheoryoflinearseriestoanumberofclassicaltopics（e…gthegeometryoftheRiemannthetadivisor）aswellastosomeofthecurrentresearchr（e.gtheKodairadimensionofthemodulispaceofcurves）．
目錄
Guide for the Reader
List of Symbols
Chapter Ⅸ.The Hilbert Scheme
1.Introduction
2.The idea of the Hilbert scheme
3.Flatness
4.Construction of the Hilbert scheme
5.The characteristic system
6.Mumford's example
7.Variants of the Hilbert scheme
8.Tangent space computations
9.Ci families of projective manifolds
10.Bibliographical notes and further reading
11.Exercises
Chapter Ⅹ.Nodal curves
1.Introduction
2.Elementary theory of nodal curves
3.Stable curves
4.Stable reduction
5.Isomorphisms of families of stable curves
6.The stable model, contraction, and projection
7.Clutching
8.Stabilization
9.Vanishing cycles and the Picard-Lefschetz transformation
10.Bibliographical notes and further reading
11.Exercises
Chapter ⅩⅠ.Elementary deformation theory and some applications
1.Introduction
2.Deformations of manifolds
3.Deformations of nodal curves
4.The concept of Kuranishi family
5.The Hilbert scheme of v-canonical curves
6.Construction of Kuranishi families
7.The Kuranishi family and continuous deformations
8.The period map and the local Torelli theorem
9.Curvature of the Hodge bundles
10.Deformations of symmetric products
11.Bibliographical notes and further reading
Chapter ⅩⅡ.The moduli space of stable curves
1.Introduction
2.Construction of moduli space as an analytic space
3.Moduli spaces as algebraic spaces
4.The moduli space of curves as an orbifold
5.The moduli space of curves as a stack, Ⅰ
6.The classical theory of descent for quasi-coherent sheaves
7.The moduli space of curves as a stack Ⅱ
8.Deligne-Mumford stacks
9.Back to algebraic spaces
10.The universal curve, projections and clutchings
11.Bibliographical notes and further reading
12.Exercises
Chapter ⅩⅢ Line bundles on moduli
1.Introduction
2.Line bundles on the moduli stack of stable curves
3.The tangent bundle to moduli and related constructions
4.The determinant of the cohomology and some applications
5.The Deligne pairing
6.The Picard group of moduli space
7.Mumford's formula
8.The Picard group of the hyperelliptic locus
9.Bibliographical notes and further reading
Chapter ⅩⅣ.Projectivity of the moduli space of stable curves
1.Introduction
2.A little invariant theory
3.The invariant-theoretic stability of linearly stable smooth curves
4.Numerical inequalities for families of stable curves
5.Projectivity of moduli spaces
6.Bibliographical notes and further reading
Chapter ⅩⅤ. The Teichmuller point of view
Chapter ⅩⅥ. Smooth Galois covers of moduli spaces
Chapter ⅩⅦ. Cycles in the moduli spaces of stable curves
Chapter ⅩⅧ. Cellular decomposition of moduli spaces
Chapter ⅩⅨ. First consequences of the cellular decomposition
Chapter ⅩⅩ. Intersection theory of tautological classes
Chapter ⅩⅩⅠ. Brill-Noether theory on a moving curve
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