English

The category of toric stacks

Algebraic Geometry 2014-01-14 v4 Combinatorics

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.

Keywords

Cite

@article{arxiv.math/0610548,
  title  = {The category of toric stacks},
  author = {Isamu Iwanari},
  journal= {arXiv preprint arXiv:math/0610548},
  year   = {2014}
}

Comments

the final version appeared in Compositio Math

R2 v1 2026-07-22T17:44:30.298Z