曲线模

出版时间：2011-4  出版社：世界图书出版公司  作者：哈里斯 (JoeHarris) IanMorrison 著  页数：366  

内容概要

　  《曲线模》是Springer数学研究生教材系列之一，全面而深入地讲述了曲线模这个科目，即代数曲线及其在族中是如何变化的。《曲线模》对曲线模的讲述，符合学习理解的规律，也是对该领域的广泛而简洁的概述，使得具有现代代数几何背景的读者很容易学习理解。书中包括了许多技巧，如Hilbert空间，变形原理，稳定约化，相交理论，几何不变理论等，曲线模型的讲述涉及从例子到应用。文中继而讨论了曲线模空间的构成，通过有限线性系列说明了Brill-Noether和Gieseker-Petri定理证明的典型应用，也讲述了一些有关不可约性，完全子变量，丰富除子和Kodaira维数的重要几何结果。书中也包括了该领域相当重要的重要定理几何开放性问题，但只是做了简明引入，并没有展开讨论。书中众多的练习和图例，使得内容更加丰富，易于理解。

书籍目录

preface1 parameter spaces： constructions and examplesa parameters and modulib construction of the hfibert schemec tangent space to the hilbert schemed extrinsic pathologiesmumford's exampleother examplese dimension of the hilbert schemef severi varietiesg hurwitz schemesbasic facts about moduli spaces of curvesa why do fine moduli spaces of curves not exist？b moduli spaces we'll be concerned withc constructions of mgthe teichmiiller approachthe hodge theory approachthe geometric invariant theory （g.i，t.） approachd geometric and topological propertiesbasic propertieslocal propertiescomplete subvarieties of mgcohomology of mg： hater's theoremscohomology of the universal curvecohomology of hfibert schemesstructure of the tautological ringwitten's conjectures and kontsevich's theoreme moduli spaces of stable mapstechniquesa basic facts about nodal and stable curvesdualizing sheavesautomorphismsb deformation theoryoverviewdeformations of smooth curvesvariations on the basic deformation theory planuniversal deformations of stable curvesdeformations of mapsc stable reductionresultsexamplesd interlude： calculations on the moduli stackdivisor classes on the moduli stackexistence of tautological familiese grothendieck-riemann-roch and porteousgrothendieck-riemann-rochchern classes of the hodge bundlechern class of the tangent bundleporteous' formulathe hyperelliptic locus in m3relations amongst standard cohomology classesdivisor classes on hilbert schemesf test curves： the hyperelliptic locus in m3 begung admissible coversh the hyperelliptic locus in m3 completed4 construction of m3a background on geometric invariant theorythe g.i.t. strategyfinite generation of and separation by invariantsthe numerical criterionstability of plane curvesb stability of hilbert points of smooth curvesthe numerical criterion for hilbert pointsgieseker's criterionstability of smooth curvesc construction of mg via the potential stability theoremthe plan of the construction and a few corollariesthe potential stability theoremlimit linear series and brill-noether theorya introductory remarks on degenerationsb limits of line bundlesc limits of linear series： motivation and examplesd limit linear series： definitions and applicationslimit linear seriessmoothing limit linear serieslimits of canonical series and weierstrass pointslimit linear series on flag curvesinequalities on vanishing sequencesthe case p = 0proof of the gieseker-petri theoremgeometry of moduli spaces： selected resultsa irreducibility of the moduli space of curvesb diaz' theoremthe idea： stratifying the moduli spacethe proofc moduli of hyperelliptic curvesfiddling aroundthe calculation for an （almost） arbitrary familythe picard group of the hyperelliptic locusd ample divisors on mgan inequality for generically hilbert stable familiesproof of the theoreman inequality for families of pointed curvesample divisors on mge irreducibility of the severi varietiesinitial reductionsanalyzing a degenerationan examplecompleting the argumentf kodaira dimension of mgwriting down general curvesbasic ideaspulling back the divisors drdivisors on mg that miss j（m2，1 \ w）divisors on mg that miss i（m0，g）further divisor class calculationscurves defined over qbibliographyindex

用户评论 (总计3条)

•   用代数几何的观点讲的，
•   非常不错，讲的比较清楚。
•   普林斯顿大学数学研究丛书中的一册