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Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes by Ballico, E.; Bernardi, A. is a scholarly article available to read on EtoBox.

What is Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes about?

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.

Author

Ballico, E.; Bernardi, A.

Published

2010

Language

EN