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Toric stacks II: Intrinsic characterization of toric stacks


Authors: 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
Published electronically: July 25, 2014
MathSciNet review: 3280037
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Abstract | References | Similar Articles | Additional Information

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
Email: satriano@umich.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06064-9
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.
Article copyright: © Copyright 2014 Anton Geraschenko and Matthew Satriano

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