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.

Orbifold cohomology for global quotients / Fantechi, B; Gottsche, L. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 117:2(2003), pp. 197-227. [10.1215/S0012-7094-03-11721-4]

Orbifold cohomology for global quotients

Fantechi, B;
2003-01-01

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.
2003
117
2
197
227
https://arxiv.org/abs/math/0104207
Fantechi, B; Gottsche, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12992
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