Orbifold Cohomology of the Symmetric Product

Chen and Ruan's orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) between the orbifold cohomology of the symmetric product of a smooth projective surface with trivial canonical class X and the cohomology of its Hilbert scheme is obtained, yielding a positive answer to a conjecture of Ruan.

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Published 1 January 2005