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.
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