Duke Mathematical Journal

Orbifold cohomology for global quotients

Barbara Fantechi and Lothar Göttsche

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Let $X$ be an orbifold that is a global quotient of a manifold $Y$ by a finite group $G$. We construct a noncommutative ring $H\sp \ast(Y, G)$ with a $G$-action such that $H\sp*(Y, G)\sp G$ is the orbifold cohomology ring of $X$ defined by W. Chen and Y. Ruan [CR]. When $Y=S\sp n$, with $S$ a surface with trivial canonical class and $G = \mathfrak {S}\sb n$, we prove that (a small modification of) the orbifold cohomology of $X$ is naturally isomorphic to the cohomology ring of the Hilbert scheme $S\sp {[n]}$, computed by M. Lehn and C. Sorger [LS2].

Article information

Duke Math. J. Volume 117, Number 2 (2003), 197-227.

First available in Project Euclid: 26 May 2004

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Zentralblatt MATH identifier

Primary: 14F25: Classical real and complex (co)homology
Secondary: 14Cxx: Cycles and subschemes 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]


Fantechi, Barbara; Göttsche, Lothar. Orbifold cohomology for global quotients. Duke Math. J. 117 (2003), no. 2, 197--227. doi:10.1215/S0012-7094-03-11721-4. http://projecteuclid.org/euclid.dmj/1085598369.

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