紧复曲面 : 第2版

21.hilbert modular surfacescoverings22.invariants of double coverings23.an enriques surface24.kummer coveringsvi.the enriques kodaira classification1.statement of the main result2.characterising minimal surfaces whose canonical bundle isnef3.the rationality theorem and castelnuovo's criterion4 the casea(x)= 25.the casea(x)= 16.thecase a(x)=07.the final step8.deformationsvii.surfaces of general typepreliminaries1.introduction2.some general theoremstwo inequalities3.noether's inequality4.the inequality c＜3c2pluricanonical maps5.the main results6.proof of the main results7.the exceptional cases and the 1-canonical mapsurfaces with given chern numbers8.the geography of chern numbers9.surfaces on the noether lines10.surfaces with q = pg = 0viii.k3-surfaces and enrlques surfacesintroduction1.notation2.the resultsk 3-surfaces3.topological and analytical invariats4.digresmon on affine geometry over f25.the neron-severl lattice of kummer surfaces6.the tore]ii theorem for kummer surfaces7.the local torelli theorem for k3-surfaces8.a density theorem9.behaviour of the kehler cone under deformations10.degenerations of isomorphisms between k3-surfaces11.the toreui theorems for k3-surfaces12.construction of moduli spaces13.digression on quaternionic structures14.surjectivity of the period mapenriques surfaces15.topological and analytic invariants16.divisors on an enriques surface y17.elliptic pencils18.double coverings of quadrics19.the period map20.the period domain for enriques surfaces21.global properties of the period map special topics22.projective k3-surfaces and mirror symmetry23.special curves on k3-surfaces24.an application to hyperbolic geometryix.topological and differentiable structure of surfacestopology of simply connected compact complex surfaces1.freedman's results2.representability of unimodular formsdonaldson invaxiants3.introduction4.the donaldson invariant, a bird's eye view5.infinitely many homeomorphic surfaces which are not diffeomorphic..6.further results obtained by the donaldson methodseiberg-witten invariants7.introduction8.properties of the invariants9.surfaces diffeomorphic to a rational surfacebibliographynotationindex

　　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。