Wall-crossing on the universal compactified Jacobian: the Theta divisor


The moduli space of line bundles on a curve can be non-compact even when the worst singularities of the curve are nodes. A natural compactification is obtained by adding stable rank-1 torsion-free sheaves: such compactification depends on the choice of a polarization on the nodal curve. Similarly, when compactifying the universal Jacobian over the moduli space of stable curves, one obtains a family of compact birational moduli spaces that depend on a polarization parameter. In this talk I will present a wall-crossing formula that describes how the theta divisor varies as a function of this parameter. This is a joint work with Jesse Kass (South Carolina).