# 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.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-00814126
Contributor : Laurent Evain <>
Submitted on : Tuesday, April 16, 2013 - 3:37:50 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM

### Identifiers

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

### Citation

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

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