Déformations équivariantes des courbes stables I : Étude cohomologique

Details Déformations équivariantes des courbes stables I : Étude cohomologique Déformations équivariantes des courbes stables I : Étude cohomologique

2003-10-09

arxiv.org/abs/math/0310137v1

Mathematics

Algebraic Geometry

31 pages, french

Scientific paper

Let $k$ be a field, $C\to \Spec k$ be a stable curve and let $G$ be a finite group acting faithfully on the curve $C\to \Spec k$. In this article, we compute the vector space $\Ext^1_G(\Omega_{C/k}, \O_C)$, the sheaf $\Omega_{C/k}$ being the sheaf of relative differentials. This vector space is naturally isomorphic to the set of first order $G$-equivariant deformations of $C$. The computation we do here will be used in a future article.

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