Speaker
Nicola Pagani
Abstract
If C is a smooth curve of genus g, there is a natural Brill-Noether cycle W_d of codimension g-d in the moduli space of degree-d line bundles J^d, which consists of those line bundles that admit a nonzero global section. This definition extends to families, producing a codimension g-d universal Brill-Noether cycle W_{g,n}^d in the degree-d universal Jacobian J^d_{g,n} over the moduli space of curves M_{g,n}.
The moduli space of curves M_{g,n} can be extended to a complete moduli space parametrising stable curves. Several different compactifications of the universal Jacobian exist, and the cycle W_{g,n}^d can be extended to each of them by means of the Thom-Porteous formula. In this talk we will discuss how to compare two extensions on two different compactifications in terms of some natural classes. This is a joint work with Alex Abreu.