代数曲线几何-第2卷 第2分册 内容简介

这是一部讲述代数曲线几何的专著，分为3卷，内容综合，全面，自成体系。本书是这部专著的下册，致力于代数曲线模理论的基础研究，作者均是在代数曲线几何发展中起到过积极作用的数学家。这门科目当发展繁荣，活跃，不仅体现在数学领域，而且体现在在和理论物理的交叉领域。手法特殊，将代数几何、复解析和拓扑/组合论很好地融合在一起，重点讲述了Teichmüller理论、模的胞状分解和Witten连通。丰富严谨的材料对想学习这么学科的学生和科研人员都是弥足珍贵的。

代数曲线几何-第2卷 第2分册 本书特色

阿尔巴雷洛所著的《代数曲线几何(第2卷第2分册)(英文版)》是一部讲述代数曲线几何的专著，致力于代数曲线模理论的基础研究，作者是在代数曲线几何发展中起到过积极作用的数学家。这门科目当发展繁荣，活跃，不仅体现在数学领域，而且体现在在和理论物理的交叉领域。手法特殊，将代数几何、复解析和拓扑/组合论很好地融合在一起，重点讲述了Teichmüller理论、模的胞状分解和Witten连通。丰富严谨的材料对想学习这门学科的学生和科研人员都是弥足珍贵的。

代数曲线几何-第2卷 第2分册 目录

GuidefortheReader
ListofSymbols
ChapterⅨ.TheHilbertScheme
1.Introduction
2.TheideaoftheHilbertscheme
3.Flatness
4.ConstructionoftheHilbertscheme
5.Thecharacteristicsystem
6.Mumford'sexample
7.VariantsoftheHilbertscheme
8.Tangentspacecomputations
9.Cnfamiliesofprojectivemanifolds
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.Constructionof'modulispaceasananalvticSDace
3.Modulispacesasalgebraicspaces
4.Themodulispaceofcurvesasanorbifold
5.Themodulispaceofcurvesasastack，I.
6.heclassicaltheoryofdescentforquasi-coherentsheaves
7.Themodulispaceofcurvesasastack，Ⅱ
8.Deligne-Mumfordstacks
9.Backtoalgebraicspaces
10.Theuniversalcurve，projectionsandclutchings
11.Bibliographicalnotesandfurtherreading
12.Exercises
ChapterⅩⅢ.Linebundlesonmoduli
1.Introduction
2.Linebundlesonthemodulistackofstablecurves
3.Thetangentbundletomoduliandrelatedconstructions
4.ThedeterminantofthecohomologyandsomeaDDlications
5.TheDelignepairing
6.ThePicardgroupofmodulispace
7.Mumford'sformula
8.ThePicardgroupofthehyperellipticlocus
9.Bibliographicalnotesandfurtherreading
ChapterⅩⅣ.Projectivityofthemodulispaceofstable
1.Introduction
2.Alittleinvarianttheory
3.Theinvariant-theoreticstabilityoflinearlystablesmoothcurves
4.Numericalinequalitiesforfamiliesofstablecurves
5.Projectivityofmodulispaces
6.Bibliographicalnotesandfurtherreading
ChapterⅩⅤ.TheTeichmullerpointofview
1.Introduction
2.Teichmullerspaceandthemappingclassgroup
3.Alittlesurfacetopology
4.QuadraticdifferentialsandTeichmullerdeformations
5.Thegeometryassociatedtoaquadraticdifferential
6.TheproofofTeichmuller'suniquenesstheorem
7.Simpleconnectednessofthemodulistackofstablecurves
8.GoingtotheboundaryofTeichmullerspace
9.Bibliographicalnotesandfurtherreading
10.Exercises
ChapterⅩⅥ.SmoothGaloiscoversofmodulispaces
1.Introduction
2.Levelstructuresonsmoothcurves
3.Automorphismsofstablecurves
4.Compactifyingmoduliofcurveswithlevelstructure，afirstattempt
5.AdmissibleG-covers
6.Automorphismsofadmissiblecovers
7.SmoothcoversofMq
8.Totallyunimodularlattices
9.SmoothcoversofMg，n
10.Bibliographicalnotesandfurtherreading
11.Exercises
ChapterⅩⅦ.Cyclesinthemodulispacesofstablecurves
1.Introduction
2.Algebraiccyclesonquotientsbyfinitegroups
3.Tautologicalclassesonmodulispacesofcurves
4.Tautologicalrelationsandthetautologicalring
5.Mumford'srelationsfortheHodgeclasses
6.Furtherconsiderationsoncyclesonmodulispaces
7.TheChowringofMO，P
8.Bibliographicalnotesandfurtherreading
9.Exercises
ChapterⅩⅧ.Cellulardecompositionofmodulispaces
1.Introduction
2.Thearcsystemcomplex
3.Ribbongraphs
4.TheideabehindthecellulardecompositionofMg，n
5.Uniformization
6.Hyperbolicgeometry
7.Thehyperbolicspineandthedefinitionofψ
8.TheequivariantcellulardecompositionofTeichmullerspace
9.Stableribbongraphs
10.ExtendingthecellulardecompositiontoapartialcompactificationofTeichmullerspace
11.Thecontinuityofψ
12.Oddsandends
13.Bibliographicalnotesandfurtherreading
ChapterⅪⅩ.Firstconsequencesofthecellulardecomposition
1.Introduction
2.ThevanishingtheoremsfortherationalhomologyofMg，p
3.ComparingthecohomologyofMg，ntotheoneofitsboundarystrata
4.ThesecondrationalcohomologygroupofMg，n
5.AquickoverviewofthestablerationalcohomologyofMg，nandthecomputationofH1（Mg，n）andH2（Mg.n）
6.Acloserlookattheorbicelldecompositionofmodulispaces
7.Combinatorialexpressionfortheclassesψi
8.Avolumecomputation
9.Bibliographicalnotesandfurtherreading
10.Exercises
ChapterⅩⅩ.Intersectiontheoryoftautologicalclasses
1.Introduction
2.Witten'sgeneratingseries
3.VirasorooperatorsandtheKdVhierarchy
4.Thecombinatorialidentity
5.Feynmandiagramsandmatrixmodels
6.Kontsevich'smatrixmodelandtheeauationL2Z=0
7.Anonvanishingtheorem
8.AbriefreviewofequivariantcohomologyandthevirtualEuler-Poincarecharacteristic
9.ThevirtualEuler-PoincarecharacteristicofMg，n
10.AveryquicktourofGromov-Witteninvariants
11.Bibliographicalnotesandfurtherreading
12.Exercises
ChapterⅩⅪ.Brill-Noethertheoryonamovingcurve
1.Introduction
2.TherelativePicardvariety
3.Brill-Noethervarietiesonmovingcurves
4.Looijenga'svanishingtheorem
5.TheZariskitangentspacestotheBrill-Noethervarieties
6.Theμ1homomorphism
7.Lazarsfeld'sproofofPetri'sconjecture
8.ThenormalbundleandHorikawa'stheory
9.Ramification
10.Planecurves
11.TheHurwitzschemeanditsirreducibility
12.Planecurvesandg1d's
13.Unirationalityresults
14.Bibliographicalnotesandfurtherreading
15.Exercises
Bibliography
Index

代数曲线几何-第2卷 第2分册 作者简介

Enrico Arbarello是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。