Orbifold Cohomology of the Symmetric Product

2001/09/18 by Bernardo Uribe, Uribe, Bernardo
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT

paper · pdf · doi:10.48550/arxiv.math/0109125

Latex

arxiv created 2001/09/18 · arxiv updated 2009/11/30

Abstract

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) H_orb^*(Xⁿ/S_n;\complex) ≅ H^*(X^[n];\complex) 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 X^[n] is obtained, yielding a positive answer to a conjecture of Ruan.

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