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

2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 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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Journal articles

Cited literature [27 references]

https://hal.inria.fr/inria-00610522
Contributor : Alessandra Bernardi Connect in order to contact the contributor
Submitted on : Monday, November 28, 2011 - 6:34:08 PM
Last modification on : Thursday, August 4, 2022 - 4:52:37 PM
Long-term archiving on: : Thursday, March 30, 2017 - 7:43:53 PM

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• HAL Id : inria-00610522, version 2

### Citation

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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