Quadratic differentials and equivariant deformation theory of curves
Quadratic differentials and equivariant deformation theory of curves
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.
quadratic differentials, tangent space, equivariant deformation functor, galois modules, riemann-roch spaces, weakly ramified, p-rank representation
1-29
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Kontogeorgis, Aristides
33932f40-5b6b-42d5-86d9-7e59829f1641
October 2012
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Kontogeorgis, Aristides
33932f40-5b6b-42d5-86d9-7e59829f1641
Koeck, Bernhard and Kontogeorgis, Aristides
(2012)
Quadratic differentials and equivariant deformation theory of curves.
Annales de l'Institut Fourier, 62 (3), .
Abstract
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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Published date: October 2012
Keywords:
quadratic differentials, tangent space, equivariant deformation functor, galois modules, riemann-roch spaces, weakly ramified, p-rank representation
Organisations:
Pure Mathematics, Mathematics
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Local EPrints ID: 148689
URI: http://eprints.soton.ac.uk/id/eprint/148689
ISSN: 1777-5310
PURE UUID: 8b81d34a-9a61-4090-a6a5-62cfb8930a4a
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Date deposited: 29 Apr 2010 09:55
Last modified: 14 Mar 2024 02:46
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Author:
Aristides Kontogeorgis
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