Natalie Hobson : Vector Bundles of Conformal Blocks-- Rank One and Finite Generation

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Sept. 28, 2016, 4 p.m.

In

SEO 427

Abstract

Given a simple Lie algebra \g, a positive integer l and an n-tuple of dominant integral weights for \g at level l, one can define a vector bundle on the moduli space of curves known as a vector bundle of conformal blocks. These bundles are nef in the case that the genus is zero and so this family provides potentially an infinite number of elements in Nef(M_0,n\bar) to analyze. It is natural to ask how this infinite family of conformal blocks divisors lives in Nef(M_0,n\bar). Is the subcone generated by conformal blocks divisors polyhedral? In this talk, we give several results to this question for specific cases of interest. To show our results, we use a correspondence of the ranks of these bundles with computations in the quantum cohomology of the Grassmannian.