UBC Algebra and Algebraic Geometry Seminar: Dustin Ross

If X is a smooth complete variety, then the alternating sums of dimensions of sheaf cohomology groups gives an additive map from the Grothendieck group of vector bundles on X to the integers. If X is not complete, then sheaf cohomology groups are generally infinite-dimensional, so we shouldn’t expect such an additive map to exist. Nonetheless, motivated by recent results in matroid theory, we introduce and study a class of incomplete toric varieties for which an analogue of this additive map still exists. I will discuss structural results about these special toric varieties, as well as generalizations of the Hirzebruch-Riemann-Roch formula and Brion’s localization formula. This talk covers joint work (some ongoing) with subsets of Matt Beck, Melody Chan, Emily Clader, and Carly Klivans.