Quelques résultats sur les déformations équivariantes des courbes stables

  • Sylvain MaugeaisEmail author


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).


Number Theory Algebraic Geometry Topological Group 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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