Back to Algebraic Geometry Seminar: Spring 2012
Algebraic Geometry Seminar
Date: Tuesday, Apr 10, 2012
Time: 3:30PM - 4:30PM
Location: LCB 222
Melissa Liu
Columbia University
Title |
Moduli spaces of real and quaternionic vector bundles over a real algebraic curve |
Abstract |
Moduli spaces of semi-stable real and quaternionic vector bundles of fixed topological type over a smooth real algebraic curve can be expressed as Lagrangian quotients and embedded into the symplectic quotient corresponding to the moduli variety of semi-stable algebraic vector bundles of fixed rank and degree on the complexified curve. When the rank and degree are coprime, these Lagrangian quotients are connected components of the real locus of the complex moduli variety endowed with the real structure induced from the real structure of the complex curve. The presentation as a quotient enables us to generalize the methods of Atiyah and Bott to a setting with involutions, and compute the mod 2 Poincare polynomials of these moduli spaces of real and quaternionic vector bundles in the coprime case. This is based on joint work with Florent Schaffhauser. |
Algebraic Geometry