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紧复曲面

版次：1
页数：
字数：
印刷时间：2011年04月01日
开本：24开
纸张：胶版纸
包装：平装
是否套装：否
国际标准书号ISBN：9787510033018

作者:（德）巴斯　著出版社:世界图书出版公司出版时间:2011年04月

内容简介

　　本书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 Seiber Witten 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
historical note
the contents of the book
standard notation
i.preliminaries
topology and algebra
1.notation and basic facts
2.some properties of bilinear forms
3.vector bundles, characteristic classes and the indextheorem
complex manifolds
4.basic concepts and facts
5.holomorphic vector bundles, serre duality and riemann-roch
6.line bundles and divisors
7.algebraic dimension and kodaira dimension

introduction 
historical note 
the contents of the book 
standard notation 
i.preliminaries 
topology and algebra 
1.notation and basic facts 
2.some properties of bilinear forms 
3.vector bundles, characteristic classes and the index
theorem 
complex manifolds 
4.basic concepts and facts 
5.holomorphic vector bundles, serre duality and riemann-roch 
6.line bundles and divisors 
7.algebraic dimension and kodaira dimension 
general analytic geometry 
8.complex spaces 
9.the a-process 
10.deformations of complex manifolds 
differential geometry of complex manifolds 
11.de rham cohomology 
12.dolbeault cohomology 
13.kaihler manifolds 
14.weight-1 hodge structures 
15.yau's results on kaihler-einstein metrics 
coverings 
16.ramification 
17.cyclic coverin 
18.covering tricks 
projective-algebraic varieties 
19.gaga theorems and projectivity criteria 
20.theorems of bertini and lefschetz 
ii.curves on surfaces 
embedded curves 
1.some standard exact sequences 
2.the picard-group of an embedded curve 
3.piemann-roch for an embedded curve 
4.the residue theorem 
5.the trace map 
6.serre duality on an embedded curve 
7.the a-process 
8.simple singularities of curves 
intersection theory 
9.intersection multiplicities 
10.intersection numbers 
11.the arithmetical genus of an embedded curve 
12.1-connected divisors 
iii.mappings of surfaces 
bimeromorphic geometry 
1.bimeromorphic maps 
2.exceptional curves 
3.rational singularities 
4.exceptional curves of the first kind 
5.hirzebruch-jung singularities 
6.resolution of surface singularities 
7.singularities of double coverings, simple singularities of
surfaces 
fibrations of surfaces 
8.generalities on fibratious 
9.the n-th root fibration 
10.stable fibrations 
11.direct image sheaves 
12.relative duality 
the period map of stable fibrations 
13.period matrices of stable curves 
14.topological monodromy of stable fibrations 
15.monodromy of the period matrix 
16.extending the period map 
17.the degree of f.ωx/s 
18.iitaka's conjecture c2,1 
iv.some general properties of surfaces 
1.meromorphic maps, associated to line bundles 
2.hodge theory on surfaces 
3.existence of kahler metrics 
4.deformations of surfaces 
5.some inequalities for hodge numbers 
6.projectivity of surfaces 
7.the nef cone 
8.surfaces of algebraic dimension zero 
9.almost-complex surfaces without any complex structure 
10.bogomolov's theorem 
11.reider's method 
12.vanishing theorems on surfaces 
v.examples 
some classical examples 
1.the projective plane p2 
2.complete intersections 
3.tori of dimension 2 
fibre bundles 
4.ruled surfaces 
5.elliptic fibre bundles 
6.higher genus fibre bundles 
elliptic fibrations 
7.kodaira's table of singular fibres 
8.stable fibrations 
9.the jacobian fibration 
10.stable reduction 
11.classification 
12.invariants 
13.logarithmic transformations 
kodaira fibrations 
14.kodaira fibrations 
finite quotients 
15.the godeaux surface 
16.kummer surfaces 
17.quotients of products of curves 
infinite quotients 
18.hopf surfaces 
19.inoue surfaces 
20.quotients of bounded domains in c: 
21.hilbert modular surfaces 
coverings 
22.invariants of double coverings 
23.an enriques surface 
24.kummer coverings 
vi.the enriques kodaira classification 
1.statement of the main result 
2.characterising minimal surfaces whose canonical bundle is
nef 
3.the rationality theorem and castelnuovo's criterion 
4 the casea(x)= 2 
5.the casea(x)= 1 
6.thecase a(x)=0 
7.the final step 
8.deformations 
vii.surfaces of general type 
preliminaries 
1.introduction 
2.some general theorems 
two inequalities 
3.noether's inequality 
4.the inequality c＜3c2 
pluricanonical maps 
5.the main results 
6.proof of the main results 
7.the exceptional cases and the 1-canonical map 
surfaces with given chern numbers 
8.the geography of chern numbers 
9.surfaces on the noether lines 
10.surfaces with q = pg = 0 
viii.k3-surfaces and enrlques surfaces 
introduction 
1.notation 
2.the results 
k 3-surfaces 
3.topological and analytical invariats 
4.digresmon on affine geometry over f2 
5.the neron-severl lattice of kummer surfaces 
6.the tore]ii theorem for kummer surfaces 
7.the local torelli theorem for k3-surfaces 
8.a density theorem 
9.behaviour of the kehler cone under deformations 
10.degenerations of isomorphisms between k3-surfaces 
11.the toreui theorems for k3-surfaces 
12.construction of moduli spaces 
13.digression on quaternionic structures 
14.surjectivity of the period map 
enriques surfaces 
15.topological and analytic invariants 
16.divisors on an enriques surface y 
17.elliptic pencils 
18.double coverings of quadrics 
19.the period map 
20.the period domain for enriques surfaces 
21.global properties of the period map special topics 
22.projective k3-surfaces and mirror symmetry 
23.special curves on k3-surfaces 
24.an application to hyperbolic geometry 
ix.topological and differentiable structure of surfaces 
topology of simply connected compact complex surfaces 
1.freedman's results 
2.representability of unimodular forms 
donaldson invaxiants 
3.introduction 
4.the donaldson invariant, a bird's eye view 
5.infinitely many homeomorphic surfaces which are not diffeomorphic
.. 
6.further results obtained by the donaldson method 
seiberg-witten invariants 
7.introduction 
8.properties of the invariants 
9.surfaces diffeomorphic to a rational surface 
bibliography 
notation 
index

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