Revista Matemática Iberoamericana

Group actions on Jacobian varieties

Anita M. Rojas

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 23, Number 2 (2007), 397-420.

Dates
First available in Project Euclid: 26 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1190831216

Mathematical Reviews number (MathSciNet)
MR2371432

Zentralblatt MATH identifier
1139.14026

Subjects
Primary: 14H40: Jacobians, Prym varieties [See also 32G20] 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]

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

Citation

Rojas, Anita M. Group actions on Jacobian varieties. Rev. Mat. Iberoamericana 23 (2007), no. 2, 397--420. https://projecteuclid.org/euclid.rmi/1190831216


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