Quelques résultats sur les déformations équivariantes des courbes stables

被引：0

作者：

Maugeais S. ^{[1
]}

机构：

[1] SFB 478, Geometrische Strukturen in der Mathematik, 48149 Münster

来源：

manuscripta mathematica | 2006年 / 120卷 / 1期

关键词：

Number Theory; Algebraic Geometry; Topological Group;

D O I：

10.1007/s00229-006-0633-2

中图分类号：

学科分类号：

摘要：

Let G be a finite group, let g ≥ 2 and g′l ≥ 0 be integers. We introduce the algebraic stack [InlineMediaObject not available: see fulltext.] classifying the stable curves [InlineMediaObject not available: see fulltext.] of genus g endowed with an action of G faithful in each geometric fiber and such that the quotient of each fiber is a semi-stable curve of genus g′. We study the completion of the local rings of this algebraic stack. They are closely related to universal equivariant deformation rings R C,G of stable curves [InlineMediaObject not available: see fulltext.] endowed with a faithful action of G. A useful tool for this purpose is a local-global principle generalizing the one obtained by Bertin and Mézard in [BM00]. We then use the results we already proved in [Mau03b] and [Mau03a] to describe some properties of the space [InlineMediaObject not available: see fulltext.] (purity, dimension). © Springer-Verlag 2006.

引用

页码：53 / 82

页数：29

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