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The orbifold Chow ring of toric Deligne-Mumford stacks

Lev A. Borisov·Linda Chen·Gregory G. Smith
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Abstract

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. 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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Lev A. Borisov, Linda Chen, Gregory G. Smith. 2003-09-14. The orbifold Chow ring of toric Deligne-Mumford stacks. https://doi.org/10.1090/s0894-0347-04-00471-0

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