Classification of compactified Jacobians over nodal curves

Abstract: If X is a smooth proper curve, then the Jacobian of X is a classical and well-studied object in algebraic geometry. When X is singular, the moduli space of degree 0 line bundles is rarely compact, and over the last century many efforts have been made to study the modular compactifications of this space, which we call "compactified Jacobians of X". In this talk we focus on the case when X has at worst nodal singularities. Some compactified Jacobians cannot arise as limits of Jacobians of smooth curves - we regard them as exotic objects. We will see that, if one excludes these exotic cases, then one can give a simple and complete combinatorial classification of all compactified Jacobians. This is based on work of myself with Tommasi, on a paper by Viviani, and on work in progress with Fava and Viviani.

mathematical physicsalgebraic geometrygeometric topology

Audience: researchers in the topic

Richmond Geometry Meeting 2024

Series comments: The Richmond Geometry Meeting will focus on emergent research topics while bringing together researchers in algebraic geometry, low-dimensional topology, and mathematical physics. In summer 2024, we will highlight developments in Geometric Topology and Moduli.

Zoom meeting id: 835 6496 8395 password: RGMVCU2024