Equivariant Todd Classes for Toric Varieties

TL;DR

This paper provides an explicit combinatorial formula for the localized equivariant Todd class of complete toric varieties, leveraging the fan structure and equivariant Riemann-Roch theorem.

Contribution

It introduces a new explicit formula for equivariant Todd classes of toric varieties based on fan data, advancing computational methods in algebraic geometry.

Findings

Derived an explicit formula for equivariant Todd classes

Connected Todd classes to fan combinatorics

Enhanced computational tools for toric varieties

Abstract

For a complete toric variety, we obtain an explicit formula for the localized equivariant Todd class in terms of the combinatorial data -- the fan. This is based on the equivariant Riemann-Roch theorem and the computation of the equivariant cohomology and equivariant homology of toric varieties.