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Article Dans Une Revue Sarajevo Journals of Mathematics Année : 2012

A partial stratification of secant varieties of Veronese varieties via curvilinear subschemes

Résumé

We give a partial ''~quasi-stratification~'' of the secant varieties of the order $d$ Veronese variety $X_{m,d}$ of $\mathbb {P}^m$. It covers the set $\sigma _t(X_{m,d})^{\dagger}$ of all points lying on the linear span of curvilinear subschemes of $X_{m,d}$, but two ''~quasi-strata~'' may overlap. For low border rank two different ''~quasi-strata~'' are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each $P\in \sigma _t(X_{m,d})^{\dagger}$ the minimal label of a quasi-stratum containing it.
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Dates et versions

inria-00610522 , version 1 (22-07-2011)
inria-00610522 , version 2 (28-11-2011)

Identifiants

  • HAL Id : inria-00610522 , version 2

Citer

Edoardo Ballico, Alessandra Bernardi. A partial stratification of secant varieties of Veronese varieties via curvilinear subschemes. Sarajevo Journals of Mathematics, 2012, 8, 1, pp.33-52. ⟨inria-00610522v2⟩
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