The orbifold Chow ring of toric Deligne-Mumford stacks
Authors:
Lev A. Borisov, Linda Chen and Gregory G. Smith
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
Published electronically:
November 3, 2004
MathSciNet review:
2114820
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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Additional 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
Keywords:
Deligne-Mumford stack,
Chow ring,
toric variety,
crepant resolution
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.
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
