In this article we study the inverse of the period map for the family F of complex algebraic curves of genus 6 equipped with an automorphism of order 5. This is a family with 2 parameters, and is fibred over a certain type of Del Pezzo surace. The period satisfies the hypergeometric differential equation for Appell's F1(3 5 , 3 5 , 2 5 , 6 5) of two… (More)
In this article we generalize the CM method for elliptic and hy-perelliptic curves to Picard curves. We describe the algorithm in detail and discuss the results of our implementation.
We explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex… (More)
We show that the Prym map for 4-th cyclicétale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.