D\'eformations \'equivariantes des courbes stables I : \'Etude cohomologique

Sylvain Maugeais

D\'eformations \'equivariantes des courbes stables I : \'Etude cohomologique

Algebraic Geometry 2007-05-23 v1 Number Theory

Authors: Sylvain Maugeais

Abstract

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.

Keywords

stable curve finite group action equivariant deformation ext group relative differentials cohomology

Cite

@article{arxiv.math/0310137,
  title  = {D\'eformations \'equivariantes des courbes stables I : \'Etude cohomologique},
  author = {Sylvain Maugeais},
  journal= {arXiv preprint arXiv:math/0310137},
  year   = {2007}
}

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31 pages, french

D\'eformations \'equivariantes des courbes stables I : \'Etude cohomologique

Abstract

Keywords

Cite

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