代数曲线几何（第2卷 第1分册）

图书标准信息

• 作者 [意]E.阿尔巴雷洛（Enrico Arbarello） 著
• 出版社 世界图书出版公司
• 出版时间 2014-08
• 版次 1
• ISBN 9787510075919
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 328页
• 正文语种 英语

【内容简介】

　　《代数曲线几何（第2卷第1分册）》是英文版的代数曲线的书。代数几何是现代数学的一个重要分支学科。它的基本研究对象是在任意维数的（仿射或射影）空间中，由若干个代数方程的公共零点所构成的集合的几何特性。这样的集合通常叫做代数簇，而这些方程叫做这个代数簇的定义方程组。

【目录】

GuidefortheReader
ListofSymbols
ChapterⅨ.TheHilbertScheme
1.Introduction
2.TheideaoftheHilbertscheme
3.Flatness
4.ConstructionoftheHilbertscheme
5.Thecharacteristicsystem
6.Mumford'sexample
7.VariantsoftheHilbertscheme
8.Tangentspacecomputations
9.Cifamiliesofprojectivemanifolds
10.Bibliographicalnotesandfurtherreading
11.Exercises

ChapterⅩ.Nodalcurves
1.Introduction
2.Elementarytheoryofnodalcurves
3.Stablecurves
4.Stablereduction
5.Isomorphismsoffamiliesofstablecurves
6.Thestablemodel,contraction,andprojection
7.Clutching
8.Stabilization
9.VanishingcyclesandthePicard-Lefschetztransformation
10.Bibliographicalnotesandfurtherreading
11.Exercises

ChapterⅩⅠ.Elementarydeformationtheoryandsomeapplications
1.Introduction
2.Deformationsofmanifolds
3.Deformationsofnodalcurves
4.TheconceptofKuranishifamily
5.TheHilbertschemeofv-canonicalcurves
6.ConstructionofKuranishifamilies
7.TheKuranishifamilyandcontinuousdeformations
8.TheperiodmapandthelocalTorellitheorem
9.CurvatureoftheHodgebundles
10.Deformationsofsymmetricproducts
11.Bibliographicalnotesandfurtherreading

ChapterⅩⅡ.Themodulispaceofstablecurves
1.Introduction
2.Constructionofmodulispaceasananalyticspace
3.Modulispacesasalgebraicspaces
4.Themodulispaceofcurvesasanorbifold
5.Themodulispaceofcurvesasastack,Ⅰ
6.Theclassicaltheoryofdescentforquasi-coherentsheaves
7.ThemodulispaceofcurvesasastackⅡ
8.Deligne-Mumfordstacks
9.Backtoalgebraicspaces
10.Theuniversalcurve,projectionsandclutchings
11.Bibliographicalnotesandfurtherreading
12.Exercises

ChapterⅩⅢLinebundlesonmoduli
1.Introduction
2.Linebundlesonthemodulistackofstablecurves
3.Thetangentbundletomoduliandrelatedconstructions
4.Thedeterminantofthecohomologyandsomeapplications
5.TheDelignepairing
6.ThePicardgroupofmodulispace
7.Mumford'sformula
8.ThePicardgroupofthehyperellipticlocus
9.Bibliographicalnotesandfurtherreading

ChapterⅩⅣ.Projectivityofthemodulispaceofstablecurves
1.Introduction
2.Alittleinvarianttheory
3.Theinvariant-theoreticstabilityoflinearlystablesmoothcurves
4.Numericalinequalitiesforfamiliesofstablecurves
5.Projectivityofmodulispaces
6.Bibliographicalnotesandfurtherreading

ChapterⅩⅤ.TheTeichmullerpointofview
ChapterⅩⅥ.SmoothGaloiscoversofmodulispaces
ChapterⅩⅦ.Cyclesinthemodulispacesofstablecurves
ChapterⅩⅧ.Cellulardecompositionofmodulispaces
ChapterⅩⅨ.Firstconsequencesofthecellulardecomposition
ChapterⅩⅩ.Intersectiontheoryoftautologicalclasses
ChapterⅩⅩⅠ.Brill-Noethertheoryonamovingcurve