Orbifold cohomology for global quotients

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 surfac...

Full description

Saved in:
Bibliographic Details
Published in:Duke mathematical journal 2003-04, Vol.117 (2), p.197-227
Main Authors: Fantechi, Barbara, Göttsche, Lothar
Format: Article
Language:English
Subjects:
14Cxx
14F25
14L24
14L30
14M17
14N35
Classical real and complex (co)homology
Cycles and subschemes
Donaldson-Thomas invariants [See also 53D45]
Gopakumar-Vafa invariants
Gromov-Witten invariants
Group actions on varieties or schemes (quotients) [See also 13A50
quantum cohomology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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].
ISSN:0012-7094
1547-7398
DOI:10.1215/S0012-7094-03-11721-4