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Orbifold cohomology for global quotients

Barbara Fantechi·Lothar Goettsche
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Abstract

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant part. In the case thar Y is S^n for a surface S with trivial canonical class we prove that (a small modification of) the orbifold cohomology of X is naturally isomorphic to the cohomology ring of the Hilbert scheme of n points on S computed in math.AG/0012166 by Lehn and Sorger.

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Barbara Fantechi, Lothar Goettsche. 2001-04-30. Orbifold cohomology for global quotients. https://arxiv.org/abs/math/0104207

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