Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes

E. Ballico; A. Bernardi

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arXiv · 1010.3546

Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes

E. Ballico·A. Bernardi

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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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BibTeX RIS

E. Ballico, A. Bernardi. 2010-10-18. Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes. https://arxiv.org/abs/1010.3546

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