Toric Hirzebruch-Riemann-Roch via Ishida's theorem on the Todd genus

TL;DR

This paper provides a straightforward proof of the Hirzebruch-Riemann-Roch theorem for smooth complete toric varieties, leveraging Ishida's theorem that the Todd genus equals one for such varieties.

Contribution

It introduces a simplified proof of the Hirzebruch-Riemann-Roch theorem specifically for smooth complete toric varieties using Ishida's result.

Findings

Todd genus of smooth complete toric varieties is one

Simplified proof of Hirzebruch-Riemann-Roch theorem

Connection between Todd genus and toric geometry

Abstract

We give a simple proof of the Hirzebruch-Riemann-Roch theorem for smooth complete toric varieties, based on Ishida's result that the Todd genus of a smooth complete toric variety is one.