Algebraic Geometry Seminar
Dima Arinkin
University of Wisconsin
Autoduality of Jacobians for singular curves
Abstract: Let C be a (smooth projective algebraic) curve. It is well known that the Jacobian J of C is a principally polarized abelian variety. In other words, J is self-dual in the sense that J is identified with the space of topologically trivial line bundles on itself.
Suppose now that C is singular. The Jacobian J of C parametrizes topologically trivial line bundles on C; it is an algebraic group which is no longer compact. By considering torsion-free sheaves instead of line bundles, one obtains a natural singular compactification J' of J.
In this talk, I consider (projective) curves C with planar singularities. The main result is that J' is self-dual: J' is identified with a space of torsion-free sheaves on itself. This autoduality naturally fits into the framework of the geometric Langlands conjecture; I hope to sketch this relation in my talk.
Wednesday March 13, 2013 at 4:00 PM in SEO 427