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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
