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Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard KöckAristides Kontogeorgis — 2012

Annales de l’institut Fourier

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...

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