The category of toric stacks

Abstract

In this paper, we prove that there exists an equivalence between 2-category of smooth Deligne-Mumford stacks with torus-embeddings and actions, and the 1-category of stacky fans. For this purpose, we obtain two main results. The first is to investigate a combinatorial aspect of the 2-category of toric algebraic stacks defined in \cite{I2}. We establish an equivalence between the 2-category of toric algebraic stacks and the 1-category of stacky fans. The second is to give a geometric characterization theorem for toric algebraic stacks.

the final version appeared in Compositio Math

References in corpus (1)

• The orbifold Chow ring of toric Deligne-Mumford stacks

Cited by in corpus (6)

• A Mirror Theorem for Toric Stacks
• The nonequivariant coherent-constructible correspondence for toric stacks
• Functorial destackification of tame stacks with abelian stabilisers
• Foliations modeling nonrational simplicial toric varieties
• Toric Stacks I: The Theory of Stacky Fans
• Toric Stacks II: Intrinsic Characterization of Toric Stacks