Open Access
August, 2007 Group actions on Jacobian varieties
Anita M. Rojas
Rev. Mat. Iberoamericana 23(2): 397-420 (August, 2007).


Consider a finite group $G$ acting on a Riemann surface $S$, and the associated branched Galois cover $\pi_G:S \to Y=S/G$. We introduce the concept of \emph{geometric signature} for the action of $G$, and we show that it captures much information: the geometric structure of the lattice of intermediate covers, the isotypical decomposition of the rational representation of the group $G$ acting on the Jacobian variety $JS$ of $S$, and the dimension of the subvarieties of the isogeny decomposition of $JS$. We also give a version of Riemann's existence theorem, adjusted to the present setting.


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Anita M. Rojas . "Group actions on Jacobian varieties." Rev. Mat. Iberoamericana 23 (2) 397 - 420, August, 2007.


Published: August, 2007
First available in Project Euclid: 26 September 2007

zbMATH: 1139.14026
MathSciNet: MR2371432

Primary: 14H40 , 14L30

Keywords: geometric signature , group actions , Jacobian varieties , Riemann surfaces , Riemann's existence theorem

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 2 • August, 2007
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