The Integral Chow Ring of Smooth Non-strict Toric Stacks

TL;DR

This paper generalizes the integral Chow ring description to smooth non-strict toric stacks by extending the Stanley-Reisner ring to non-strict stacky fans and proving their isomorphism.

Contribution

It introduces an extension of the Stanley-Reisner ring to non-strict stacky fans and proves its isomorphism with the integral Chow ring of the associated toric stack.

Findings

The extended Stanley-Reisner ring is isomorphic to the integral Chow ring.

Generalizes known results to a broader class of toric stacks.

Provides a new algebraic tool for studying non-strict toric stacks.

Abstract

We extend the Stanley-Reisner ring to the non-strict stacky fans introduced by Geraschenko and Satriano. We then prove that this ring is isomorphic to the integral Chow ring of the smooth non-strict toric stack defined by the given non-strict stacky fan. This generalizes known results for the integral Chow rings of less general toric stacks.