Data di Pubblicazione:
2018
Citazione:
Shimura curves in the Prym locus / E. Colombo, P. Frediani, A. Ghigi, M. Penegini. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - (2018 Mar 13), pp. 1850009.1850009-1-1850009.1850009-34. [Epub ahead of print]
Abstract:
We study Shimura curves of PEL type in Ag generically contained in the Prym locus. We study both the unramified Prym locus, obtained using ´etale 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 1-dimensional and the quotient of the base curve by the group is P1. 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 gotten in this way up to genus 28. We obtain 44 Shimura curves generically contained in the unramified Prym locus and 9 families generically contained in the ramified Prym locus. Most of these curves are not generically contained in the Jacobian locus.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Shimura varieties; Prym varieties; Prym locus
Elenco autori:
E. Colombo, P. Frediani, A. Ghigi, M. Penegini
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