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Quelques résultats sur les déformations équivariantes des courbes stables

  • Sylvain MaugeaisEmail author
Article

Abstract

Let G be a finite group, let g≥2 and g ′ ≥ 0 be integers. We introduce the algebraic stack Open image in new window classifying the stable curves Open image in new window 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 Open image in new window 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 Open image in new window (purity, dimension).

Keywords

Number Theory Algebraic Geometry Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.SFB 478 - Geometrische Strukturen in der MathematikMünsterGermany

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