Orbifold Cohomology of the Symmetric Product

Bernardo Uribe

Orbifold Cohomology of the Symmetric Product

Algebraic Topology 2007-05-23 v1 Algebraic Geometry

Authors: Bernardo Uribe

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) $H_{orb}^*(X^n/S_n;\complex) \cong H^*(X^{[n]};\complex)$ 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.

Keywords

orbifold cohomology symmetric product hilbert scheme complex manifold ring isomorphism

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@article{arxiv.math/0109125,
  title  = {Orbifold Cohomology of the Symmetric Product},
  author = {Bernardo Uribe},
  journal= {arXiv preprint arXiv:math/0109125},
  year   = {2007}
}

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Orbifold Cohomology of the Symmetric Product

Abstract

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