We outline a method to compute the type of the induced polarization of an abelian subvariety of a canonically polarized Jacobian of a smooth projective curve. The method works for curves of not too big genus admitting a ...

Given a compact Riemann surface X with an action of a finite group G, the group algebra provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to ...

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many ...

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 much ...

We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups G(q),3 of order 3(q) ...

We obtain a characterization of theta functions of Jacobian varieties of curves with automorphisms among theta functions of principally polarized abelian varieties (p p a v) We first give a characterization m terms of ...

Given a closed Riemann surface R of genus p >= 2 together with an anticonformal involution tau : R -> R with fixed points, we consider the group K(R, tau) consisting of the conformal and anticonformal auto-morphisms of R ...

The isogenous decomposition of the Jacobian variety of classical Fermat curve of prime degree p >= 5 has been obtained by Aoki using techniques of number theory, by Barraza and Rojas in terms of decompositions of the algebra ...

In this talk we present a generalisation of the well-known theorem of Kani and Rosen on decomposition of Jacobian varieties of Riemann surfaces with group action. This result lengthens the set of Jacobians for which it is ...