A homological approach for computing the tangent space of the deformation functor of curves with automorphisms

Details A homological approach for computing the tangent space of the deformation functor of curves with automorphisms A homological approach for computing the tangent space of the deformation functor of curves with automorphisms

2003-12-24

arxiv.org/abs/math/0312447v1

Mathematics

Algebraic Geometry

Scientific paper

We give an alternative approach to the computation of the dimension of the tangent space of the deformation space of curves with automorphisms. A homological version of the local-global principle similar to the one of J.Bertin, A. M\'ezard is proved, and a computation in the case of ordinary curves is obtained, by application of the results of S. Nakajima for the Galois module structure of the space of 2-holomorphic differentials on them.

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