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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Duke Mathematical Journal
( Vol. 117 NO.2 / (2003))
Orbifold Cohomology for Global Quotients
Barbara Fantechi, Lothar Gottsche,
Pages. 197-227
Abstract Let $X$ be an orbifold that is a global quotient a manifold $Y$ by a finite group $G$. We construct a noncommutative ring $H^ast (Y, G)$ with a $G$-action such that $H^ast (Y, G)^G$ is the orbifold cohomology ring of $X$ defined by W. Chen and Y. Ruan [CR]. When $Y = S^n$, with $S$ a surface with trivial canonical class and $G = G_n$, we prove that (a small modification of) the orbifold cohomology of $X$ is naturally isomorphic to the cohomology ring of the Hilbert scheme $S^{[n]}$, computed by M. Lehn and C. Sorger [SL2].
Contents Introduction 1. Orbifold cohomology for a quotient orbifold 2. Orbifold cohomology and crepant resolutions 3. The case of the symmetric product 4. Generalized Kummer varieties
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Mathmatical Subject Classification 14C05, 14F25, 14H20, 14L30, 14