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L'anneau de cohomologie des résolutions crépantes de certaines singularités-quotient

Abstract : The geometric quotient of a smooth variety under a volume-preserving action of a finite group is singular. The McKay correspondence relates the geometry of the crepant resolutions of the quotient and the geometry of the action on the smooth variety. Under some conditions, the equivariant Hilbert scheme of the smooth variety is a crepant resolution. We interpret this scheme as an equivariant grassmannian of algebras, so as to deduce its explicit description. According to Ruan's conjecture, the cohomology ring of a crepant resolution is isomorphic to the orbifold cohomology ring of the quotient, modulo a quantic deformation. For the quotient of a three-dimensional variety, local (linear space with linear action) or compact, we compute the cohomology ring of the crepant resolutions. In the local case, an example shows that the quantic deformation is necessary in Ruan's conjecture. In the compact case, the analogy between the two rings reinforces Ruan's conjecture.
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https://tel.archives-ouvertes.fr/tel-00158942
Contributor : Sébastien Garino <>
Submitted on : Monday, July 2, 2007 - 9:57:26 AM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Monday, September 24, 2012 - 10:47:09 AM

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Sébastien Garino. L'anneau de cohomologie des résolutions crépantes de certaines singularités-quotient. Mathématiques [math]. Université de Nantes, 2007. Français. ⟨tel-00158942⟩

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