Gavril Farkas
Humboldt University

Title: Models of the Prym moduli space via special K3 surfaces

Abstract: In a series of well-known papers from the nineties, Mukai
dicovered new models for the moduli space M_g of curves of genus g<12, by
using moduli of K3 surfaces. In joint work with A. Verra, we present a
striking analogy of this type of result at the level of the Prym moduli
space R_g and many of Mukai's results for M_g, have precise Prym
counterparts. Via K3 surfaces of Nikulin type, we show that R_g has a
Nikulin-Mukai model for g<8 (which establishes the unirationality of R_g
in this range), while R_7 has the structure of a Mori fibre space over the
moduli space of Nikulin surfaces. We finally establish the uniruledness of
R_8, which is the highest genus where such a result is known to hold.