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內容簡介: |
代数几何和算术代数几何是现代数学的重要分支,与数学的许多分支有着广泛的联系,如数论、解析几何、微分几何、交换代数、代数群、拓扑学等。代数几何是任何一个希望在数学学科有所作为的学生和研究人员需要了解的一门学科,而模空间是代数几何最重要的一类对象。
《模手册(卷2)(英文版)》是由50多位活跃在代数几何领域的世界知名专家撰写的综述性文章组成。每一篇文章针对一个专题,作者力求将第一手、最新鲜的材料呈现给读者,通过介绍该专题中基础知识、例子和结论,带领读者快速进入该领域,并了解领域内重要问题;同时介绍最新的进展,使得读者能够很快捕捉到该领域最主要的文献。
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目錄:
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VolumeⅠ
Preface
GavrilFarkasandIanMorrison
Logarithmicgeometryandmoduli
DanAbramorrich,QileChen,DannyGillam,YuhaoHuang,MartinOlsson,MatthewSatrianoandShenghaoSun
InvariantHilbertschemes
MichelBrion
Algebraicandtropicalcurves:comparingtheirmodulispaces
LuciaCaporaso
Asuperficialworkingguidetodeformationsandmoduli
F.Catanese
ModulispacesofhyperbolicsurfacesandtheirWeil-Peterssonvolumes
NormanDo
Equivariantgeometryandthecohomologyofthemodulispaceofcurves
DanEdidin
Tautologicalandnon-tautologicalcohomologyofthemodulispaceofcurves
C.FaberandR.Pandharipande
Alternatecompaaificationsofmodulispacesofcurves
MaksymFedorchuhandDavidIshiiSmyth
ThecohomologyofthemodulispaceofAbelianvarieties
GerardvanderGeer
ModuliofK3surfacesandirreduciblesymplecticmanifolds
VGritsenko,K.HulekandC.K.Sanharan
Normalfunctionsandthegeometryofmodulispacesofcurves
RichardHain
VolumeⅡ
Parameterspacesofcurves
JoeHarris
GlobaltopologyoftheHitchinsystem
TamasHausel
Differentialformsonsingularspaces,theminimalmodelprogram,andhyperboliatyofmodulistacks
StefanKebekus
ContractibleextremalraysonMo,n
SeanKeelandJamesMeKernan
Moduliofvarietiesofgeneraltype
JanosKollar
Singularitiesofstablevarieties
SandorJKovacs
SolitonequationsandtheRiemann-Schottkyproblem
I.KricheverandT.Shiota
GITandmoduliwithatwist
RaduLaza
Gooddegenerationsofmodulispaces
JunLi
LocalizationinGromov-WittentheoryandOrbifoldGromov-Wittentheory
Chiu-ChuMelissaLiu
FromWZWmodelstomodularfunctors
EduardLooijenga
Shimuravarietiesandmoduli
J.S.Milne
TheTorellilocusandspecialsubvarieties
BenMoonenandFransOort
VolumeⅢ
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