Descrizione
ABSTRACT: First introduced by F. Prym and then revived by D. Mumford, Prym varieties are abelian varieties obtained from finite étale covers of smooth curves. Over the moduli space of such covers, one can thus consider a universal family of Prym varieties. J. Harris and D. Mumford showed that moduli of étale covers can be compactified by allowing certain controlled degenerations called admissible covers. The universal Prym variety can be naturally extended over the moduli space of admissible covers, alas the resulting space is not compact. Can we find a modular compactification? This is a joint work with A. Gross, J. Horn, S. Molcho and M. Ulirsch.