  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.
