Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard Köck[1]; Aristides Kontogeorgis[2]

  • [1] University of Southampton School of Mathematics Highfield Southampton SO17 1BJ (United Kingdom)
  • [2] National and Kapodistrian University of Athens Department of Mathematics Panepistimioupolis GR-157 84 Athens (Greece)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 1015-1043
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Köck, Bernhard, and Kontogeorgis, Aristides. "Quadratic Differentials and Equivariant Deformation Theory of Curves." Annales de l’institut Fourier 62.3 (2012): 1015-1043. <http://eudml.org/doc/251036>.

@article{Köck2012,
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.},
affiliation = {University of Southampton School of Mathematics Highfield Southampton SO17 1BJ (United Kingdom); National and Kapodistrian University of Athens Department of Mathematics Panepistimioupolis GR-157 84 Athens (Greece)},
author = {Köck, Bernhard, Kontogeorgis, Aristides},
journal = {Annales de l’institut Fourier},
keywords = {quadratic differentials; tangent space; equivariant deformation functor; Galois modules; Riemann-Roch spaces; weakly ramified; $p$-rank representation},
language = {eng},
number = {3},
pages = {1015-1043},
publisher = {Association des Annales de l’institut Fourier},
title = {Quadratic Differentials and Equivariant Deformation Theory of Curves},
url = {http://eudml.org/doc/251036},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Köck, Bernhard
AU - Kontogeorgis, Aristides
TI - Quadratic Differentials and Equivariant Deformation Theory of Curves
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 1015
EP - 1043
AB - 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.
LA - eng
KW - quadratic differentials; tangent space; equivariant deformation functor; Galois modules; Riemann-Roch spaces; weakly ramified; $p$-rank representation
UR - http://eudml.org/doc/251036
ER -

References

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