# The orbifold Chow ring of toric Deligne-Mumford stacks

@article{Borisov2004TheOC, title={The orbifold Chow ring of toric Deligne-Mumford stacks}, author={Lev Borisov and Linda Chen and Gregory G. Smith}, journal={Journal of the American Mathematical Society}, year={2004}, volume={18}, pages={193-215} }

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.

## 277 Citations

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Abstract We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a “torus”. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms…

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We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a ''torus''. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of…

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