Back to Algebraic Geometry Seminar: Fall 2011
Algebraic Geometry Seminar
Date: Tuesday, Nov 15, 2011
Time: 3:30PM - 4:30PM
Location: LCB 222
Dave Anderson
University of Washington
Title |
Okounkov bodies, toric degenerations, and polytopes |
Abstract |
Given a projective variety X of dimension d, a “flag” of subvarieties Y_i, and a big divisor D, Okounkov showed how to construct a convex body in R^d, and in the last few years, this construction has been developed further in work of Kaveh-Khovanskii and Lazarsfeld-Mustata. In general, the Okounkov body is quite hard to understand, but when X is a toric variety, it is just the polytope associated to D via the standard yoga of toric geometry. I’ll describe a more general situation where the Okounkov body is still a polytope, and show that in this case X admits a flat degeneration to the corresponding toric variety. As an application, I’ll describe some toric degenerations of flag varieties and Schubert varieties, and explain how the Okounkov bodies arising generalize the Gelfand-Tsetlin polytopes. |
Algebraic Geometry