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內容簡介

《麯綫模》是Springer數學研究生教材係列之一，全麵而深入地講述瞭麯綫模這個科目，即代數麯綫及其在族中是如何變化的。《麯綫模》對麯綫模的講述，符閤學習理解的規律，也是對該領域的廣泛而簡潔的概述，使得具有現代代數幾何背景的讀者很容易學習理解。書中包括瞭許多技巧，如Hilbert空間，變形原理，穩定約化，相交理論，幾何不變理論等，麯綫模型的講述涉及從例子到應用。文中繼而討論瞭麯綫模空間的構成，通過有限綫性係列說明瞭Brill-Noether和Gieseker-Petri定理證明的典型應用，也講述瞭一些有關不可約性，完全子變量，豐富除子和Kodaira維數的重要幾何結果。書中也包括瞭該領域相當重要的重要定理幾何開放性問題，但隻是做瞭簡明引入，並沒有展開討論。書中眾多的練習和圖例，使得內容更加豐富，易於理解。

目錄

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

前言/序言

麯綫模 [Moduli of Curves] 下載 mobi epub pdf txt 電子書

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