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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.
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Preprints, Working Papers, ...
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Contributor : Laurent Evain Connect in order to contact the contributor
Submitted on : Tuesday, April 16, 2013 - 3:37:50 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:43 AM

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



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



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