Back to Algebraic Geometry Seminar: Fall 2009
Algebraic Geometry Seminar
Date: Tuesday, Nov 17, 2009
Time: 3:30PM - 4:30PM
Location: LCB 225
David Treumann
Northwestern University
Title |
The coherent-constructible correspondence for toric varieties |
Abstract |
This is a talk on joint work with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow. An equivariant ample line bundle on a toric variety determines a polytope in a real vector space. I will discuss work we have done to extend this familiar correspondence to an equivalence of categories, between the derived category of coherent sheaves on the toric variety and a derived category of polyhedrally-constructible sheaves on the real vector space. Many famous aspects of the dictionary between toric geometry and polyhedral combinatorics are visible in this equivalence. Work of Nadler and Zaslow relates the second category to a Fukaya category of Lagrangian submanifolds of a symplectic vector space. Thus our correspondence can be viewed as a verification–for toric varieties–of a version of Kontsevich’s homological mirror symmetry conjecture. |
Algebraic Geometry