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Toric Stacks II: Intrinsic Characterization of Toric Stacks

Geraschenko, Anton and Satriano, Matthew (2015) Toric Stacks II: Intrinsic Characterization of Toric Stacks. Transactions of the American Mathematical Society, 367 (2). pp. 1073-1094. ISSN 0002-9947.

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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:© 2014 Anton Geraschenko and Matthew Satriano. Article electronically published on July 25, 2014. Received by the editors December 12, 2012. The second author was partially supported by NSF grant DMS-0943832. We thank Jesse Kass and Martin Olsson for conversations which helped get this project started, and Vera Serganova and the MathOverflow community (especially Torsten Ekedahl, Jim Humphreys, Peter McNamara, David Speyer, and Angelo Vistoli) for their help with several technical points. We also thank Smiley for helping to track down many references. Finally, we would like to thank the anonymous referee for helpful suggestions and interesting questions.
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Issue or Number:2
Classification Code:2010 MSC. Primary 14D23, 14M25
Record Number:CaltechAUTHORS:20150123-082201820
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Official Citation:Anton Geraschenko and Matthew Satriano Journal: Trans. Amer. Math. Soc. 367 (2015), 1073-1094 Published electronically: July 25, 2014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54006
Deposited By: Ruth Sustaita
Deposited On:23 Jan 2015 18:11
Last Modified:03 Oct 2019 07:54

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