@article{Kontoge2007JPAAp551558,
  title = {{Polydifferentials and the deformation functor of curves with automorphisms}},
  author = {Kontogeorgis, A.},
  file = {JPAA.pdf},
  volume = {210},
  pages = {551{--}558},
  url = {http://dx.doi.org/10.1016/j.jpaa.2006.10.015},
  doi = {10.1016/j.jpaa.2006.10.015},
  year = {2007},
  journal = {J. Pure Appl. Algebra},
  abstract = {We give a relation between the dimension of the tangent space of the deformation functor of curves with automorphisms and the Galois module structure of the space of 2-holomorphic differentials. We prove a homological version of the local-global principle similar to the one of J.Bertin, A. Mezard. Let G be a cyclic subgroup of the group of automorphisms of a curve X, so that the order of G is equal to the characteristic. By using the results of S. Nakajima on the Galois module structure of the space of 2-holomorphic differentials, we compute the dimension of the tangent space of the deformation functor},
  issn = {0022-4049},
  number = {2}
}