### Prym varieties of triple coverings

Ortega, A *(Humboldt)*

Thursday 24 March 2011, 14:00-15:00

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

Classical Prym varieties are principally polarised abelian varieties associated to etale double coverings between curves. We study a special class of Prym-Tjurin varieties of exponent 3, coming from non-cyclicetale triple coverings of curves of genus 2. We show that the moduli space of such coverings is a rational threefold, mapping 10:1 via the Prym map to the moduli space of principal polarised abelian surfaces. The crucial ingredient used to obtain such an explicit description of the moduli space, is that any genus 4 curve which admits a non-cyclic triple cover over a genus 2 curve, is actually hyperelliptic. We also describe the extended Prym map from the moduli space of *admissible* S_3-covers onto A_2 . This is a joint work with Herbert Lange