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. 
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