Group actions on Jacobian varieties

2003/10/10 by Anita M. Rojas, Rojas, Anita M. · 1 citation
Mathematics · #14H40 #20C05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H40 #msc:20C05

paper · pdf · doi:10.48550/arxiv.math/0310158

23 pages. Minor grammatical changes and a corrected version of the last corollary

arxiv created 2005/12/22 · arxiv updated 2009/12/01

Abstract

Consider a finite group G acting on a Riemann surface S, and the associated branched Galois cover π_G:S → Y=S/G. We introduce the concept of geometric signature for the action of G, and we show that it captures the information of the geometric structure of the lattice of intermediate covers, the information about 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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