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.
Original language | English |
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Pages (from-to) | 718-746 |
Number of pages | 29 |
Journal | Compositio Mathematica |
Volume | 145 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2009 May |
Externally published | Yes |
Keywords
- algebraic stacks
- logarithmic geometry
- toric geometry
ASJC Scopus subject areas
- Algebra and Number Theory