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Pré-Publication, Document De Travail Année : 2012

Bialynicki-Birula schemes in higher dimensional Hilbert schemes of points

Résumé

The Bialynicki-Birula cells on the Hilbert scheme H^n({A}^d) are smooth and reduced in dimension d=2. We prove that there is a schematic structure in higher dimension, the Bialynicki-Birula scheme, which is natural in the sense that it represents a functor. Let \rho_i be the Hilbert-Chow morphism from the Hilbert scheme H^n({A}^d) to Sym^n(A^1) associated with the i^{th} coordinate. We prove that a Bialynicki-Birula scheme associated with an action of a torus T is schematically included in the fiber over the origin $\rho_i^{-1}(0)$ if the i^{th} weight of T is non positive.

Dates et versions

hal-00814126 , version 1 (16-04-2013)

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Laurent Evain, Mathias Lederer. Bialynicki-Birula schemes in higher dimensional Hilbert schemes of points. 2012. ⟨hal-00814126⟩
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