On the Prym map for cyclic covers of genus two curves

Daniele Agostini

Published 2020-01-17Version 1

The Prym map assigns to each covering of curves a polarized abelian variety. In the case of cyclic covers of curves of genus two, we show that the Prym map is ramified precisely on the locus of bielliptic covers. The key observation is that we can naturally associate to such a cover an abelian surface with a cyclic polarization, and then the differential of the Prym map corresponds to multiplication of sections on the abelian surface.