| 词条 | 曲线模 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第1版 (2011年4月1日) 外文书名: Moduli of Curves 平装: 366页 正文语种: 英语 开本: 24 ISBN: 9787510032974 条形码: 9787510032974 尺寸: 22.2 x 14.8 x 1.8 cm 重量: 458 g 作者简介作者：（美国）哈里斯（Joe Harris） （美国）Ian Morrison 内容简介《曲线模(英文版)》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。 目录preface 1 parameter spaces: constructions and examples a parameters and moduli b construction of the hfibert scheme c tangent space to the hilbert scheme d extrinsic pathologies mumford's example other examples e dimension of the hilbert scheme f severi varieties g hurwitz schemes basic facts about moduli spaces of curves a why do fine moduli spaces of curves not exist? b moduli spaces we'll be concerned with c constructions of mg the teichmiiller approach the hodge theory approach the geometric invariant theory (g.i,t.) approach d geometric and topological properties basic properties local properties complete subvarieties of mg cohomology of mg: hater's theorems cohomology of the universal curve cohomology of hfibert schemes structure of the tautological ring witten's conjectures and kontsevich's theorem e moduli spaces of stable maps techniques a basic facts about nodal and stable curves dualizing sheaves automorphisms b deformation theory overview deformations of smooth curves variations on the basic deformation theory plan universal deformations of stable curves deformations of maps c stable reduction results examples d interlude: calculations on the moduli stack divisor classes on the moduli stack existence of tautological families e grothendieck-riemann-roch and porteous grothendieck-riemann-roch chern classes of the hodge bundle chern class of the tangent bundle porteous' formula the hyperelliptic locus in m3 relations amongst standard cohomology classes divisor classes on hilbert schemes f test curves: the hyperelliptic locus in m3 begun g admissible covers h the hyperelliptic locus in m3 completed 4 construction of m3 a background on geometric invariant theory the g.i.t. strategy finite generation of and separation by invariants the numerical criterion stability of plane curves b stability of hilbert points of smooth curves the numerical criterion for hilbert points gieseker's criterion stability of smooth curves c construction of mg via the potential stability theorem the plan of the construction and a few corollaries the potential stability theorem limit linear series and brill-noether theory a introductory remarks on degenerations b limits of line bundles c limits of linear series: motivation and examples d limit linear series: definitions and applications limit linear series smoothing limit linear series limits of canonical series and weierstrass points limit linear series on flag curves inequalities on vanishing sequences the case p = 0 proof of the gieseker-petri theorem geometry of moduli spaces: selected results a irreducibility of the moduli space of curves b diaz' theorem the idea: stratifying the moduli space the proof c moduli of hyperelliptic curves fiddling around the calculation for an (almost) arbitrary family the picard group of the hyperelliptic locus d ample divisors on mg an inequality for generically hilbert stable families proof of the theorem an inequality for families of pointed curves ample divisors on mg e irreducibility of the severi varieties initial reductions analyzing a degeneration an example completing the argument f kodaira dimension of mg writing down general curves basic ideas pulling back the divisors dr divisors on mg that miss j(m2,1 \\ w) divisors on mg that miss i(m0,g) further divisor class calculations curves defined over q bibliography index |
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