紧复曲面：英文

图书标准信息

• 作者 [德]巴斯 著
• 出版社 世界图书出版公司
• 出版时间 2011-04
• 版次 2
• ISBN 9787510033018
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 436页
• 正文语种 英语
• 原版书名 Compact Complex Surfaces(Second Enlarged Edition)

【内容简介】

《紧复曲面（第2版）》是一部非常好的学习代数曲面的书，提供了复曲面分类的复解析方法。此书是从复代数几何角度研究复曲面的大全类书籍，从初等入门到高深前沿都有涉及。这本书是经典中的经典，讲的是代数曲面的各种专题，每个章节都写的无限完美。内容包括曲面里的曲线，相交数，霍奇分解，pojectivity，有理曲面分类，Kodaira分类，general曲面，K3&Enrique曲面。此书新版的最后两章写的尤其好，一是K3曲面；另一个是Doanaldson和SeiberWitten理论，后者是来自模空间的不变量理论，都是现在热门的专题。有位读者这么说：“可以说如果学代数几何没念过这本书，甚至是学几何没念过《紧复曲面（第2版）》，可以考虑换行，是百年难得一见的好书。“可见《紧复曲面（第2版）》书在该领域具有举足轻重的地位。

【目录】

introduction
historicalnote
thecontentsofthebook
standardnotation
i.preliminaries
topologyandalgebra
1.notationandbasicfacts
2.somepropertiesofbilinearforms
3.vectorbundles,characteristicclassesandtheindextheorem
complexmanifolds
4.basicconceptsandfacts
5.holomorphicvectorbundles,serredualityandriemann-roch
6.linebundlesanddivisors
7.algebraicdimensionandkodairadimension
generalanalyticgeometry
8.complexspaces
9.thea-process
10.deformationsofcomplexmanifolds
differentialgeometryofcomplexmanifolds
11.derhamcohomology
12.dolbeaultcohomology
13.kaihlermanifolds
14.weight-1hodgestructures
15.yau'sresultsonkaihler-einsteinmetrics
coverings
16.ramification
17.cycliccoverin
18.coveringtricks
projective-algebraicvarieties
19.gagatheoremsandprojectivitycriteria
20.theoremsofbertiniandlefschetz
ii.curvesonsurfaces
embeddedcurves
1.somestandardexactsequences
2.thepicard-groupofanembeddedcurve
3.piemann-rochforanembeddedcurve
4.theresiduetheorem
5.thetracemap
6.serredualityonanembeddedcurve
7.thea-process
8.simplesingularitiesofcurves
intersectiontheory
9.intersectionmultiplicities
10.intersectionnumbers
11.thearithmeticalgenusofanembeddedcurve
12.1-connecteddivisors
iii.mappingsofsurfaces
bimeromorphicgeometry
1.bimeromorphicmaps
2.exceptionalcurves
3.rationalsingularities
4.exceptionalcurvesofthefirstkind
5.hirzebruch-jungsingularities
6.resolutionofsurfacesingularities
7.singularitiesofdoublecoverings,simplesingularitiesofsurfaces
fibrationsofsurfaces
8.generalitiesonfibratious
9.then-throotfibration
10.stablefibrations
11.directimagesheaves
12.relativeduality
theperiodmapofstablefibrations
13.periodmatricesofstablecurves
14.topologicalmonodromyofstablefibrations
15.monodromyoftheperiodmatrix
16.extendingtheperiodmap
17.thedegreeoff.ωx/s
18.iitaka'sconjecturec2,1
iv.somegeneralpropertiesofsurfaces
1.meromorphicmaps,associatedtolinebundles
2.hodgetheoryonsurfaces
3.existenceofkahlermetrics
4.deformationsofsurfaces
5.someinequalitiesforhodgenumbers
6.projectivityofsurfaces
7.thenefcone
8.surfacesofalgebraicdimensionzero
9.almost-complexsurfaceswithoutanycomplexstructure
10.bogomolov'stheorem
11.reider'smethod
12.vanishingtheoremsonsurfaces
v.examples
someclassicalexamples
1.theprojectiveplanep2
2.completeintersections
3.toriofdimension2
fibrebundles
4.ruledsurfaces
5.ellipticfibrebundles
6.highergenusfibrebundles
ellipticfibrations
7.kodaira'stableofsingularfibres
8.stablefibrations
9.thejacobianfibration
10.stablereduction
11.classification
12.invariants
13.logarithmictransformations
kodairafibrations
14.kodairafibrations
finitequotients
15.thegodeauxsurface
16.kummersurfaces
17.quotientsofproductsofcurves
infinitequotients
18.hopfsurfaces
19.inouesurfaces
20.quotientsofboundeddomainsinc:
21.hilbertmodularsurfaces
coverings
22.invariantsofdoublecoverings
23.anenriquessurface
24.kummercoverings
vi.theenriqueskodairaclassification
1.statementofthemainresult
2.characterisingminimalsurfaceswhosecanonicalbundleisnef
3.therationalitytheoremandcastelnuovo'scriterion
4thecasea（x）=2
5.thecasea（x）=1
6.thecasea（x）=0
7.thefinalstep
8.deformations
vii.surfacesofgeneraltype
preliminaries
1.introduction
2.somegeneraltheorems
twoinequalities
3.noether'sinequality
4.theinequalityc＜3c2
pluricanonicalmaps
5.themainresults
6.proofofthemainresults
7.theexceptionalcasesandthe1-canonicalmap
surfaceswithgivenchernnumbers
8.thegeographyofchernnumbers
9.surfacesonthenoetherlines
10.surfaceswithq=pg=0
viii.k3-surfacesandenrlquessurfaces
introduction
1.notation
2.theresults
k3-surfaces
3.topologicalandanalyticalinvariats
4.digresmononaffinegeometryoverf2
5.theneron-severllatticeofkummersurfaces
6.thetore]iitheoremforkummersurfaces
7.thelocaltorellitheoremfork3-surfaces
8.adensitytheorem
9.behaviourofthekehlerconeunderdeformations
10.degenerationsofisomorphismsbetweenk3-surfaces
11.thetoreuitheoremsfork3-surfaces
12.constructionofmodulispaces
13.digressiononquaternionicstructures
14.surjectivityoftheperiodmap
enriquessurfaces
15.topologicalandanalyticinvariants
16.divisorsonanenriquessurfacey
17.ellipticpencils
18.doublecoveringsofquadrics
19.theperiodmap
20.theperioddomainforenriquessurfaces
21.globalpropertiesoftheperiodmapspecialtopics
22.projectivek3-surfacesandmirrorsymmetry
23.specialcurvesonk3-surfaces
24.anapplicationtohyperbolicgeometry
ix.topologicalanddifferentiablestructureofsurfaces
topologyofsimplyconnectedcompactcomplexsurfaces
1.freedman'sresults
2.representabilityofunimodularforms
donaldsoninvaxiants
3.introduction
4.thedonaldsoninvariant,abird'seyeview
5.infinitelymanyhomeomorphicsurfaceswhicharenotdiffeomorphic..
6.furtherresultsobtainedbythedonaldsonmethod
seiberg-witteninvariants
7.introduction
8.propertiesoftheinvariants
9.surfacesdiffeomorphictoarationalsurface
bibliography
notation
index