On the birational geometry of the universal compactified Jacobian

Filippo Viviani, October 22nd, 2013

We compute the Kodaira dimension and the Iitaka fibration of the universal Jacobian
parametrizing line bundles on smooth projective curves. A crucial ingredient in the proof
is the Caporaso-Pandharipande compactification and a detailed analysis of its
singularities. This is based on joint works with Bini-Fontanari and with
Casalaina-Martin-Kass.