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Quadratic differentials and equivariant deformation theory of curves

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
1777-5310
1-29
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Kontogeorgis, Aristides
33932f40-5b6b-42d5-86d9-7e59829f1641
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), 1-29.

Record type: Article

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

Identifiers

Local EPrints ID: 148689
URI: https://eprints.soton.ac.uk/id/eprint/148689
ISSN: 1777-5310
PURE UUID: 8b81d34a-9a61-4090-a6a5-62cfb8930a4a
ORCID for Bernhard Koeck: ORCID iD orcid.org/0000-0001-6943-7874

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Date deposited: 29 Apr 2010 09:55
Last modified: 26 Jul 2019 00:35

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Contributors

Author: Bernhard Koeck ORCID iD
Author: Aristides Kontogeorgis

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