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
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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