Toric stacks II: Intrinsic characterization of toric stacks
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- by Anton Geraschenko and Matthew Satriano PDF
- Trans. Amer. Math. Soc. 367 (2015), 1073-1094
Abstract:
The purpose of this paper and its prequel is to introduce and develop a theory of toric stacks which encompasses and extends several notions of toric stacks defined in the literature, as well as classical toric varieties.
While the focus of the prequel is on how to work with toric stacks, the focus of this paper is how to show a stack is toric. For toric varieties, a classical result says that a finite type scheme with an action of a dense open torus arises from a fan if and only if it is normal and separated. In the same spirit, the main result of this paper is that any Artin stack with an action of a dense open torus arises from a stacky fan under reasonable hypotheses.
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Additional Information
- Anton Geraschenko
- Affiliation: Department of Mathematics 253-37, California Institute of Technology, 1200 California Boulevard, Pasadena, California 91125
- Email: geraschenko@gmail.com
- Matthew Satriano
- Affiliation: Department of Mathematics, 2074 East Hall, University of Michigan, Ann Arbor, Michigan 48109-1043
- MR Author ID: 986189
- Email: satriano@umich.edu
- Received by editor(s): December 12, 2012
- Published electronically: July 25, 2014
- Additional Notes: The second author was partially supported by NSF grant DMS-0943832.
- © Copyright 2014 Anton Geraschenko and Matthew Satriano
- Journal: Trans. Amer. Math. Soc. 367 (2015), 1073-1094
- MSC (2010): Primary 14D23, 14M25
- DOI: https://doi.org/10.1090/S0002-9947-2014-06064-9
- MathSciNet review: 3280037