# Algebraic Geometry Seminar

#### Autoduality and Fourier-Mukai for Compactified Jacobians

**Speaker:**
Margarida Melo, University of Coimbra

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, October 22, 2013, 3:30 p.m.

**Synopsis:**

Among Abelian varieties, Jacobians of smooth curves C have the important property of being autodual, i.e., they are canonically isomorphic to their dual abelian variety. This is equivalent to the existence of a Poincare line bundle P on J(C)xJ(C) which is universal as a family of algebraically trivial line bundles on J(C). Another instance of this fact was discovered by S. Mukai who proved that the Fourier-Mukai transform with kernel P is an auto-equivalence of the bounded derived category of J(C). I will talk on joint work with Filippo Viviani and Antonio Rapagnetta, where we try to generalize both the autoduality result and Mukai's equivalence result for singular reducible curves X with locally planar singularities. Our results generalize previous results of Arinkin, Esteves, Gagne and Kleiman and can be seen as an instance of the geometric Langlands duality for the Hitchin fibration.