The orbifold Chow ring of toric Deligne-Mumford stacks

Details The orbifold Chow ring of toric Deligne-Mumford stacks The orbifold Chow ring of toric Deligne-Mumford stacks

2003-09-14

arxiv.org/abs/math/0309229v3

Journal of the American Mathematical Society 18 (2005) 193-215.

Mathematics

Algebraic Geometry

23 pages; revision improves the exposition in several places

Scientific paper

10.1090/S0894-0347-04-00471-0

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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