The chow cohomology of affine toric varieties

TL;DR

This paper investigates the Chow cohomology of affine toric varieties, demonstrating that it vanishes in positive degrees, and extends similar results to operational K-theory.

Contribution

It proves the vanishing of Chow cohomology in positive degrees for affine toric varieties and extends the result to operational K-theory.

Findings

Chow cohomology vanishes in positive degree for affine toric varieties

Operational K-theory also vanishes in positive degree for these varieties

Provides new insights into the structure of cohomology theories for toric varieties

Abstract

We study the Fulton-Macpherson Chow cohomology of affine toric varieties. In particular, we prove that the Chow cohomology vanishes in positive degree. We prove an analogous result for the operational $K$-theory defined by Anderson and Payne.