Orbifold cohomology for global quotients
Algebraic Geometry
2007-05-23 v2
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.
Cite
@article{arxiv.math/0104207,
title = {Orbifold cohomology for global quotients},
author = {Barbara Fantechi and Lothar Goettsche},
journal= {arXiv preprint arXiv:math/0104207},
year = {2007}
}
Comments
We correct a small sign error and add some references. 22 pages