# Bialynicki-Birula schemes in higher dimensional Hilbert schemes of points

Abstract : 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.
Type de document :
Pré-publication, Document de travail
20 pages. 2012

https://hal.archives-ouvertes.fr/hal-00814126
Contributeur : Laurent Evain <>
Soumis le : mardi 16 avril 2013 - 15:37:50
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04

### Identifiants

• HAL Id : hal-00814126, version 1
• ARXIV : 1209.2026

### Citation

Laurent Evain, Mathias Lederer. Bialynicki-Birula schemes in higher dimensional Hilbert schemes of points. 20 pages. 2012. 〈hal-00814126〉

### Métriques

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