Quadratic differentials and equivariant deformation theory of curves

Details Quadratic differentials and equivariant deformation theory of curves Quadratic differentials and equivariant deformation theory of curves

2011-04-18

arxiv.org/abs/1104.3539v1

Mathematics

Algebraic Geometry

30 pages, to appear in Ann. Inst. Fourier (Grenoble)

Scientific paper

Given a finite p-group G acting on a smooth projective curve X over an algebraically closed field k of characteristic p, the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of G acting on the space V of global holomorphic quadratic differentials on X. We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when G is cyclic or when the action of G on X is weakly ramified. Moreover we determine certain subrepresentations of V, called p-rank representations.

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