We study Shimura curves of PEL type in (Formula presented.) generically contained in the Prym locus. We study both the unramified Prym locus, obtained using Ã©tale double covers, and the ramified Prym locus, corresponding to double covers ramified at two points. In both cases, we consider the family of all double covers compatible with a fixed group action on the base curve. We restrict to the case where the family is one-dimensional and the quotient of the base curve by the group is (Formula presented.). We give a simple criterion for the image of these families under the Prym map to be a Shimura curve. Using computer algebra we check all the examples obtained in this way up to genus 28. We obtain 43 Shimura curves contained in the unramified Prym locus and 9 families contained in the ramified Prym locus. Most of these curves are not generically contained in the Jacobian locus.
|Titolo:||Shimura curves in the Prym locus|
|Data di pubblicazione:||2018|
|Appare nelle tipologie:||01.01 - Articolo su rivista|