On the tangent space of the deformation functor of curves with automorphisms

Abstract

We provide a method to compute the dimension of the tangent space to the global infinitesimal deformation functor of a curve together with a subgroup of the group of automorphisms. The computational techniques we developed are applied to several examples including Fermat curves, $p$-cyclic covers of the affine line and to Lehr-Matignon curves.

arXiv comment33 pages, A gap in the proof of lemma 1.5 is filled