标题：曲线模
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