Displaying similar documents to “Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere”

On the Hodge cycles of Prym varieties

Indranil Biswas (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.

On equations defining fake elliptic curves

Pilar Bayer, Jordi Guàrdia (2005)

Journal de Théorie des Nombres de Bordeaux

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Shimura curves associated to rational nonsplit quaternion algebras are coarse moduli spaces for principally polarized abelian surfaces endowed with quaternionic multiplication. These objects are also known as . We present a method for computing equations for genus 2 curves whose Jacobian is a fake elliptic curve with complex multiplication. The method is based on the explicit knowledge of the normalized period matrices and on the use of theta functions with characteristics. As in the...