Geometria Moduli of curves on Enriques surfaces Andreas Leopold Knutsen 17-12-2020 - 14:30 modalità telematica
Curves on K3 surfaces have been studied a lot and play a relevant role in the study of the moduli space of curves. By contrast, not so much has been known about curves on Enriques surfaces, except that the rich geometry of the surface (in particular the existence of many elliptic pencils) make curves on Enriques surfaces quite special from the point of view of Brill-Noether theory. Moreover, the existence of a non-trivial 2-torsion bundle on the surface (the canonical bundle) endows every curve on an Enriques surface with a natural structure of a Prym curve. I will report on joint work in collaboration with C. Ciliberto, Th. Dedieu and C. Galati (arXiv:1902.07142), where we in particular prove that, with a few exceptions, a general Prym curve lying on an Enriques surface lies on a unique such surface. The exceptions are related to the existence of Enriques-Fano threefolds and to existence of Prym curves with nodal Prym-canonical model. |