Birational classification of toric orbifolds

TL;DR

This paper provides a comprehensive classification of smooth proper toric Deligne-Mumford stacks up to torus-equivariant birational equivalence, based on their associated stacky fans.

Contribution

It introduces a complete classification framework for toric orbifolds using stacky fans, advancing understanding of their birational geometry.

Findings

Classification of toric orbifolds via stacky fans

Characterization of birational equivalence classes

Framework for analyzing toric stacks

Abstract

We give a complete classification of the torus-equivariant birational equivalence classes of smooth proper toric Deligne-Mumford stacks with trivial generic stabilizer in terms of their associated stacky fans.