Two ways of degenerating the Jacobian are the same

Series: 
Algebra Seminar
Monday, November 25, 2013 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
University of South Carolina
,  
Organizer: 
The Jacobian variety of a smooth complex curve is a complex torus that admits two different algebraic descriptions. The Jacobian can be described as the Picard variety, which is the moduli space of line bundles, or it can be described as the Albanese variey, which is the universal abelian variety that contains the curve. I will talk about how to extend a family of Jacobians varieties by adding degenerate fibers.  Corresponding to the two different descriptions of the Jacobian are two different extensions of the Jacobian: the Neron model and the relative moduli space of stable sheaves. I will explain what these two extensions are and then prove that they are equivalent. This equivalence has surprising consequences for both the Neron model and the moduli space of stable sheaves.