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Journal articles
On the equivariant cohomology of Hilbert schemes of points in the plane
Abstract : Let $S$ be the affine plane regarded as a toric variety with an action of the 2-dimensional torus $T$. We study the equivariant Chow ring $A_{K}^*(Hilb^n(S))$ of the punctual Hilbert scheme $Hilb^n(S)$ with equivariant coefficients inverted. We compute base change formulas in $A_{K}^*(Hilb^n(S))$ between the natural bases introduced by Nakajima, Ellingsrud and Str{\o}mme, and the classical basis associated with the fixed points. We compute the equivariant commutation relations between creation/annihilation operators. We express the class of the small diagonal in $Hilb^n(S)$ in terms of the equivariant Chern classes of the tautological bundle. We prove that the nested Hilbert scheme $Hilb^[n,n+1](S)$ parametrizing nested punctual subschemes of degree $n$ and $n+1$ is irreducible.
https://hal.archives-ouvertes.fr/hal-00713204
Contributor : Laurent Evain <>
Submitted on : Friday, June 29, 2012 - 3:26:59 PM
Last modification on : Wednesday, April 1, 2020 - 12:20:06 AM
Contributor : Laurent Evain <>
Submitted on : Friday, June 29, 2012 - 3:26:59 PM
Last modification on : Wednesday, April 1, 2020 - 12:20:06 AM
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