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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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The orbifold Chow ring of toric Deligne-Mumford stacks
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by Lev A. Borisov, Linda Chen and Gregory G. Smith
J. Amer. Math. Soc. 18 (2005), 193-215
DOI: https://doi.org/10.1090/S0894-0347-04-00471-0
Published electronically: November 3, 2004

Abstract:

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks. The main result in this paper is an explicit calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an application, we prove that the orbifold Chow ring of the toric Deligne-Mumford stack associated to a simplicial toric variety is a flat deformation of (but is not necessarily isomorphic to) the Chow ring of a crepant resolution.
References
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Bibliographic Information
  • Lev A. Borisov
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email: borisov@math.wisc.edu
  • Linda Chen
  • Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
  • Address at time of publication: Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, Ohio 43210
  • Email: lchen@math.ohio-state.edu
  • Gregory G. Smith
  • Affiliation: Department of Mathematics, Barnard College, Columbia University, New York, New York 10027
  • Address at time of publication: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6 Canada
  • MR Author ID: 622959
  • Email: ggsmith@mast.queensu.ca
  • Received by editor(s): September 30, 2003
  • Published electronically: November 3, 2004
  • Additional Notes: The first author was partially supported in part by NSF grant DMS-0140172.
    The second author was partially supported in part by NSF VIGRE grant DMS-9810750.
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 18 (2005), 193-215
  • MSC (2000): Primary 14N35; Secondary 14C15, 14M25
  • DOI: https://doi.org/10.1090/S0894-0347-04-00471-0
  • MathSciNet review: 2114820