紧复曲面

《紧复曲面(英文版)(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 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。

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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