K theory of smooth complete toric varieties and related spaces

TL;DR

This paper extends the algebraic K-theory description to complete non-singular toric varieties and related spaces, providing a unified framework for understanding their K-rings through generators and relations.

Contribution

It offers a new description of K-rings for complete non-singular toric varieties and torus manifolds with locally standard actions, generalizing previous results.

Findings

K-ring descriptions for complete non-singular toric varieties

Unified approach for torus manifolds with homology polytope orbit space

Extension of earlier work on quasi-toric manifolds

Abstract

The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for complete non-singular toric varieties. Indeed, our approach enables us to obtain such a description for the more general class of torus manifolds with locally standard torus action and orbit space a homology polytope.