Back to Algebraic Geometry Seminar: Fall 2015
Algebraic Geometry Seminar
Date: Tuesday, Dec 8, 2015
Time: 3:30PM - 4:30PM
Location: JFB 102
Barbara Bolognese
Northeastern University
Title |
Strange Duality and Verlinde numbers on abelian surfaces |
Abstract |
With the purpose of examining some relevant geometric properties of the moduli space of sheaves over an algebraic surface, Le Potier conjectured some unexpected duality between the complete linear series of certain natural divisors, called Theta divisors, on the moduli space. Such conjecture is widely known as Strange Duality conjecture. After having motivated the problem by looking at certain instances of quantization in physics, we will work in the setting of surfaces. We will then sketch the proof in the case of abelian surfaces, giving an idea of the techniques that are used. In particular, we will show how the theory of discrete Heisenberg groups and fiber wise Fourier-Mukai transforms, which might be applied to other cases of interest, enter the picture. |
Algebraic Geometry