Toric varieties are of interest both in their own right as algebraic varieties, and for their application to the theory of convex polytopes. For instance, Danilov used the Hirzebruch-Riemann-Roch theorem to establish a direct connection between the problem of counting the number of lattice points in a convex polytope and the Todd classes of toric varieties. In this talk, I will discuss the computation of generalized homology Todd classes of (possibly singular) toric varieties, with applications to weighted lattice point counting. In the simplicial context, I will present a formula which computes these homology classes in terms of (cohomological) "mock" characteristic classes plus explicit contributions of the singular locus. This is joint work with Joerg Schuermann.
Penn Mathematics Colloquium
Wednesday, October 1, 2014 - 4:30pm
Maxim Laurentiu
University of Wisconsin