模手册

出版时间：2012-12  出版社：高等教育出版社  作者：Gavril Farkas,Ian Morrison  页数：594  
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内容概要

　　代数几何和算术代数几何是现代数学的重要分支，与数学的许多分支有着广泛的联系，如数论、解析几何、微分几何、交换代数、代数群、拓扑学等。代数几何是任何一个希望在数学学科有所作为的学生和研究人员需要了解的一门学科，而模空间是代数几何最重要的一类对象。　　《模手册（卷2）（英文版）》是由50多位活跃在代数几何领域的世界知名专家撰写的综述性文章组成。每一篇文章针对一个专题，作者力求将第一手、最新鲜的材料呈现给读者，通过介绍该专题中基础知识、例子和结论，带领读者快速进入该领域，并了解领域内重要问题；同时介绍最新的进展，使得读者能够很快捕捉到该领域最主要的文献。

作者简介

作者：（德国）法卡斯（Gavril Farkas） （美国）莫里森（Ian Morrison）

书籍目录

Volume Ⅰ Preface Gavril Farkas and Ian Morrison Logarithmic geometry and moduli Dan Abramovich,Qile Chen,Danny Gillam,Yuhao Huang,Martin Olsson,Matthew Satriano and Shenghao Sun Invariant Hilbert schemes Michel Brion Algebraic and tropical curves:comparing their moduli spaces Lucia Caporaso A superficial working guide to deformations and moduli F.Catanese Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes Norman Do Equivariant geometry and the cohomology of the moduli space of curves Dan Edidin Tautological and non-tautological cohomology of the moduli space of curves C.Faber and R.Pandharipande Altemate compactifications of moduli spaces of curves Maksym Fedorchuk and David Ishii Smyth The cohomology of the moduli space of Abelian varieties Gerard van der Geer Moduli of K3 surfaces and irreducible symplectic manifolds V.Gritsenko,K.Hulek and G.K.Sankaran Normal functions and the geometry of moduli spaces of curves Richard Hain Volume Ⅱ Parameter spaces of curves Ioe Harris Global topology of the Hitchin system Tamás Hausel Differential forms on singular spaces,the minimal model program,and hyperbolicity of moduli stacks Stefan Kebekus Contractible extremal rays on (M)0,n Seán Keel and James McKernan Moduli of varieties of general type János Kollár Singularities of stable varieties Sándor J Kovács Soliton equations and the Riemann-Schottky problem I.Krichever and T.Shiota GIT and moduli with a twist Radu Laza Good degenerations of moduli spaces Jun Li Localization in Gromov-Witten theory and Orbifold Gromov-Witten theory Chiu-Chu Melissa Liu From WZW models to modular functors Eduard Looijenga Shimura varieties and moduli J.S. Milne The Torelli locus and special subvarieties Ben Moonen and Frans Oort Volume Ⅲ Birational geometry for nilpotent orbits Yoshinori Namikawa Cell decompositions of moduli space,lattice points and Hurwitz problems Paul Norbury Moduli of abelian varieties in mixed and in positive characteristic Frans Oort Local models of Shimura varieties,I.Geometry and combinatorics Georgios Pappas,Michael Rapoport and Brian Smithling Generalized theta linear series on moduli spaces of vector bundles on curves Mihnea Popa Computer aided unirationality proofs of moduli spaces Frank-Olaf Schreyer Deformation theory from the point of view of fibered categories Mattia Talpo and Angelo Vistoli Mumford's conjecture-a topological outlook Ulrike Tillmann Rational parametrizations of moduli spaces of curves Alessandw Verra Hodge loci Claire Voisin Homological stability for mapping class groups of surfaces Nathalie Wahl

章节摘录

版权页：   插图：   (By a simplicial cone we mean a cone over a simplex,i.e.a polyhedral cone whose edges are linearly independent) The spaces (M)0,n and (M)0,n are interesting from a number of viewpoints.They are closely related to the moduli space of curves,(M)g.A finite quotient of (M)0,n occurs as a locus of degenerate curves in the boundary of (M)g,while (M)0,n is the base of the complete Hurwitz scheme (see [2]) which can be used,for example,to prove that (M)g is irreducible.By [3],(M)0,n parametrizes degenerations of rational normal curves.Generalisations of (M)0,n are important for Quantum Cohomologycalculations,see [11].(M)0,n is useful for studying fibrations with general fibre P1,as in particular it can sometimes be used in lieu of a minimal model program.Kawamata exploits this in [5] to prove additivity of log Kodaira dimension for one dimensional fibres,and in [6] to prove a codimension two subadjunction formula. We note that there is an explicit construction of (M)0,n as a blow up of Pn-3 along a sequence of simple centres (see(3.1)).In particular (M)0,5 is a del Pezzo of degree five,(M)0,6 is log Fano, and (M)0,7 is nearly log Fano,in the sense that -K)M)0.7 is effective.We do not know of such an explicit construction of (M)0,n, and we have in general a much weaker grasp on its geometry (though a much stronger grasp on its cones).Note by (1.3.3),(M)0,nadmits no nontrivial fibrafions.See also (3.7).

编辑推荐

《模手册(卷2)(英文版)》是由50多位活跃在代数几何领域的世界知名专家撰写的综述性文章组成。