標籤: 暫無標籤

《曲線模(英文版)》是Springer數學研究生教材系列之一,全面而深入地講述了曲線模這個科目,即代數曲線及其在族中是如何變化的。《曲線模》對曲線模的講述,符合學習理解的規律,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。書中包括了許多技巧,如Hilbert空間,變形原理,穩定約化,相交理論,幾何不變理論等,曲線模型的講述涉及從例子到應用。作者為(美國)哈里斯(Joe Harris) (美國)Ian Morrison

1 曲線模 -圖書信息

  出版社: 世界圖書出版公司; 第1版 (2011年4月1日)

  外文書名: Moduli of Curves

  平裝: 366頁

  正文語種: 英語

  開本: 24

  ISBN: 9787510032974

  條形碼: 9787510032974

  尺寸: 22.2 x 14.8 x 1.8 cm

  重量: 458 g

2 曲線模 -作者簡介

  作者:(美國)哈里斯(Joe Harris) (美國)Ian Morrison

3 曲線模 -內容簡介

  《曲線模(英文版)》是Springer數學研究生教材系列之一,全面而深入地講述了曲線模這個科目,即代數曲線及其在族中是如何變化的。《曲線模》對曲線模的講述,符合學習理解的規律,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。書中包括了許多技巧,如Hilbert空間,變形原理,穩定約化,相交理論,幾何不變理論等,曲線模型的講述涉及從例子到應用。文中繼而討論了曲線模空間的構成,通過有限線性系列說明了Brill-Noether和Gieseker-Petri定理證明的典型應用,也講述了一些有關不可約性,完全子變數,豐富除子和Kodaira維數的重要幾何結果。書中也包括了該領域相當重要的重要定理幾何開放性問題,但只是做了簡明引入,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。

4 曲線模 -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

下一篇[過境鳥]

相關評論

同義詞:暫無同義詞