代数曲线几何（第2卷 第2分册）

图书标准信息

• 作者 [意]阿尔巴雷洛 著
• 出版社 世界图书出版公司
• 出版时间 2014-08
• 版次 1
• ISBN 9787510077777
• 定价 99.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 963页
• 正文语种 英语

【内容简介】

　　Thisvolumeisdevotedtothefoundationsofthetheoryofmoduliofalgebraiccurvesdefinedoverthecomplexnumbers.Thefirstvolumewasalmostexclusivelyconcernedwiththegeometryonafixed,smoothcurve.Atthetimeitwaspublished,thelocaldeformationtheoryofasmoothcurvewaswellunderstood,butthestudyofthegeometryofglobalmoduliwasinitsearlystages.Thisstudyhassinceundergoneexplosivedevelopmentandcontinuestodoso.Therearetworeasonsforthis;onepredictableatthetimeofthefirstvolume,theothernot.
　　Thepredictableonewastheintrinsicalgebro-geometricinterestinthemoduliofcurves;thishascertainlyturnedouttobethecase.Theotheristheexternalinfluencefromphysics.Becauseofthisconfluence,thesubjecthasdevelopedinwaysthatareincrediblyricherthancouldhavebeenimaginedatthetimeofwritingofVolumeI.
　　Whenthisvolume,GACII,wasplanneditwasenvisionedthatthecen-terpiecewouldbethestudyoflinearseriesonageneralorvariablecurve,culminatinginaproofofthePetriconjecture.Thisisstillanimportantpartofthepresentvolume,butitisnotthecentralaspect.Rather,themainpurposeofthebookistoprovidecomprehensiveanddetailedfoundationsforthetheoryofthemoduliofalgebraiccurves.Inaddition,wefeelthataveryimportant,perhapsdistinguishing,aspectofGACIIistheblendingofthemultipleperspectives-algebro-geometric,complex-analytic,topological,andcombinatorial-thatareusedforthestudyofthemoduliofcurves.

【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