Toric h-vectors and Chow Betti Numbers of Dual Hypersimplices

TL;DR

This paper provides explicit formulas for toric h-vectors and Chow Betti numbers related to dual hypersimplices and their normal fans, connecting combinatorial invariants with geometric cohomology in Grassmannians.

Contribution

It introduces explicit formulas for toric h-numbers and Chow Betti numbers of dual hypersimplices and their normal fans, extending to type A^* lattices.

Findings

Explicit formulas for toric h-numbers of dual hypersimplices.

Explicit formulas for Chow Betti numbers of the normal fan of a hypersimplex.

Formulas applicable to coordinator numbers of type A^* lattices.

Abstract

The toric h-numbers of a dual hypersimplex and the Chow Betti numbers of the normal fan of a hypersimplex are the ranks of intersection cohomology and Chow cohomology respectively of the torus orbit closure of a generic point in the Grassmannian. We give explicit formulas for these numbers. We also show that similar formulas hold for the coordinator numbers of type A^* lattices.