The orbifold Chow ring of toric Deligne-Mumford stacks

Borisov, Lev; Chen, Linda; Smith, Gregory

doi:10.1090/S0894-0347-04-00471-0

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
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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.

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