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

Edoardo Ballico 1 Alessandra Bernardi 2
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : 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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https://hal.inria.fr/inria-00610522
Contributor : Alessandra Bernardi Connect in order to contact the contributor
Submitted on : Friday, July 22, 2011 - 11:45:12 AM
Last modification on : Monday, October 12, 2020 - 10:27:36 AM
Long-term archiving on: : Sunday, December 4, 2016 - 10:01:14 AM

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  • HAL Id : inria-00610522, version 1

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Edoardo Ballico, Alessandra Bernardi. A partial stratification of secant varieties of Veronese varieties via curvilinear subschemes. 2011. ⟨inria-00610522v1⟩

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