Harvard-MIT Algebraic Geometry Seminar: The Chow ring of the universal Picard stack over the hyperelliptic locus

Understanding the line bundles on curves are essential to understanding the curves themselves. As such, the universal Picard stack J^d_g --> M_g parametrizing degree d line bundles on genus g curves is an important object of study. Recently, progress has been made on the intersection theory of M_g in low genus by stratifying the moduli space by gonality. The smallest piece in this stratification is the hyperelliptic locus. Motivated by this, I'll present several results about the restriction of J^d_g to the hyperelliptic locus, denoted J^d_{2,g}. These include a presentation of the rational Chow ring of J^d_{2,g}. I also determine the integral Picard group of J^d_{2,g}, completing (and extending to the PGL_2-equivariant case) prior work of Erman and Wood.