Add to ORKGInternational audienceWe 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
We describe the stratification by tensor rank of the points belonging to the tangent developable of ...
We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algeb...
This is a survey primarily about determining the border rank of tensors, especially those relevant f...
International audienceWe give a partial ''~quasi-stratification~'' of the secant varieties of the or...
If $X\subset \mathbb{P}^n$ is a projective non degenerate variety, the $X$-rank of a point $P\in \ma...
When considering $\sigma_r(X)$, the variety of r-secant $\PP {r-1}$ to a projective variety $X$, one...
If $X\subset \mathbb{P}^n$ is a projective non degenerate variety, the $X$-rank of a point $P\in \m...
We consider here the problem, which is quite classical in Algebraic Geometry, of studying the secant...
We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant...
We prove a conjecture stated by Catalisano, Geramita, and Gimigliano in 2002, which claims that the ...
We describe the stratification by tensor rank of the points belonging to the tangent developable of ...
Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $\mathbb{P}^n \times \mathbb{P}^m$ v...
International audienceWe consider the problem of determining the symmetric tensor rank for symmetric...
International audienceLet $X^{(n,m)}_{(1,d)}$ denote the Segre\/-Veronese embedding of $\PP n \times...
We describe the stratification by tensor rank of the points belonging to the tangent developable of ...
We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algeb...
This is a survey primarily about determining the border rank of tensors, especially those relevant f...
International audienceWe give a partial ''~quasi-stratification~'' of the secant varieties of the or...
If $X\subset \mathbb{P}^n$ is a projective non degenerate variety, the $X$-rank of a point $P\in \ma...
When considering $\sigma_r(X)$, the variety of r-secant $\PP {r-1}$ to a projective variety $X$, one...
If $X\subset \mathbb{P}^n$ is a projective non degenerate variety, the $X$-rank of a point $P\in \m...
We consider here the problem, which is quite classical in Algebraic Geometry, of studying the secant...
We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant...
We prove a conjecture stated by Catalisano, Geramita, and Gimigliano in 2002, which claims that the ...
We describe the stratification by tensor rank of the points belonging to the tangent developable of ...
Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $\mathbb{P}^n \times \mathbb{P}^m$ v...
International audienceWe consider the problem of determining the symmetric tensor rank for symmetric...
International audienceLet $X^{(n,m)}_{(1,d)}$ denote the Segre\/-Veronese embedding of $\PP n \times...
We describe the stratification by tensor rank of the points belonging to the tangent developable of ...
We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algeb...
This is a survey primarily about determining the border rank of tensors, especially those relevant f...