Etale double covers of cyclic p-gonal covers

Herbert Lange
Universität Erlangen-Nürnberg
I will give a report on a recent joint paper with Angel Carocca and Rubi Rodriguez. This paper computes the Galois group of the Galois cover of the composition of an étale double cover of a cyclic
-gonal cover for any prime
. Moreover a relation between some of its Prym varieties and the Jacobian of a subcover is given. In a sense this generalizes the trigonal construction.