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Sur les correspondances de McKay pour le schéma de Hilbert de points sur le plan affine

Abstract : The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of singularities and the representations of the group. For the Hilbert scheme of points in the affine plane, we study how the different correspondences (McKay, dual McKay and multiplicative McKay) are related to each other. For this purpose, we compute combinatorial formulas for the usual vector bundles on the Hilbert scheme of points in the affine plane. We also study the multiplicative behavior of the theorem of Bridgeland, King \& Reid constructing the McKay correspondence for the Hilbert scheme of points in the affine plane. We finish with the computation of the Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane.
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https://tel.archives-ouvertes.fr/tel-00007177
Contributor : Samuel Boissière <>
Submitted on : Friday, October 22, 2004 - 10:05:39 AM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Thursday, September 13, 2012 - 12:20:31 PM

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Samuel Boissière. Sur les correspondances de McKay pour le schéma de Hilbert de points sur le plan affine. Mathématiques [math]. Université de Nantes, 2004. Français. ⟨tel-00007177⟩

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