On the tangent space of the deformation functor of curves with automorphisms

Kontogeorgis, Aristides

doi:10.2140/ant.2007.1.119

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On the tangent space of the deformation functor of curves with automorphisms

Aristides Kontogeorgis

Vol. 1 (2007), No. 2, 119–161

DOI: 10.2140/ant.2007.1.119

Abstract

We provide a method to compute the dimension of the tangent space to the global infinitesimal deformation functor of a curve together with a subgroup of the group of automorphisms. The computational techniques we developed are applied to several examples including Fermat curves, $p$ -cyclic covers of the affine line and to Lehr–Matignon curves.

Keywords

automorphisms, curves, deformations

Mathematical Subject Classification 2000

Primary: 14H37

Secondary: 14D15, 14B10

Milestones

Received: 30 January 2007

Revised: 11 June 2007

Accepted: 23 July 2007

Published: 1 May 2007

Authors

Aristides Kontogeorgis
Department of Mathematics University of the Aegean Karlovassi Samos 83200
http://eloris.samos.aegean.gr

Vol. 1, No. 2, 2007