The category of toric stacks

By Isamu Iwanari. Compositio Mathematica, 2006

48 citations recorded by the source corpus.

Abstract In this paper, we show that there is an equivalence between the 2-category of smooth Deligne–Mumford stacks with torus embeddings and actions and the 1-category of stacky fans. To this end, we prove two main results. The first is related to a combinatorial aspect of the 2-category of toric algebraic stacks defined by I. Iwanari [Logarithmic geometry, minimal free resolutions and toric algebraic stacks, Preprint (2007)]; we establish an equivalence between the 2-category of toric algebraic stacks and the 1-category of stacky fans. The second result provides a geometric characterization of toric algebraic stacks. Logarithmic geometry in the sense of Fontaine–Illusie plays a central role in obtaining our results.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e9cb873f50cc9c1db4bf9f8126cdcbf53b52abe3

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Citations in the corpus

The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks (2009, background): “1], N is a free abelian group, so toric stacks in [13] are toric orbifolds.”
LOCALIZATION IN GROMOV-WITTEN THEORY AND ORBIFOLD GROMOV-WITTEN THEORY (2011, unknown): “Later, more geometric definitions of toric orbifolds and toric DM stacks are given by Iwanari [27, 28] and by Fantechi-Mann-Nironi [19], respectively.”
Smooth toric Deligne-Mumford stacks (2010, methodology): “Hence, the notion of toric orbifold is the same as the one used in [22], Theorem 1.”