The Integral (orbifold) Chow Ring of Toric Deligne-Mumford Stacks

TL;DR

This paper computes the integral Chow ring of semi-projective toric Deligne-Mumford stacks, showing it is isomorphic to the Stanley-Reisner ring, and provides explicit calculations for the orbifold Chow ring.

Contribution

It establishes an isomorphism between the integral Chow ring of certain stacks and Stanley-Reisner rings, extending previous results to the integral setting.

Findings

Integral Chow ring is isomorphic to the Stanley-Reisner ring for semi-projective stacks

Explicit computation of the integral orbifold Chow ring

Illustrative examples demonstrating the theoretical results

Abstract

In this paper we study the integral Chow ring of toric Deligne-Mumford stacks. We prove that the integral Chow ring of a semi-projective toric Deligne-Mumford stack is isomorphic to the Stanley-Reisner ring of the associated stacky fan. The integral orbifold Chow ring is also computed. Our results are illustrated with several examples.