Polydifferentials and the deformation functor of curves with   automorphisms II
  We apply the known results on the Galois module structure of the sheaf of polydifferentials in order to study the dimension of the tangent space of the deformation functor of curves with automorphisms. We are able to find the dimension for the case of weakly ramified covers and for the case of the action of a cyclic group of order $p^v$. 
Kontogeorgis Aristides