Group actions on Jacobian varieties

الأصل · EN

Consider a finite group G acting on a Riemann surface S, and the associated branched Galois cover πG: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.