Geodesic
On the third secant variety
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 2, pp. 475-502.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We determine normal forms and ranks of tensors of border rank at most three. We present a differential-geometric analysis of limits of secant planes in a more general context. In particular there are at most four types of points on limiting trisecant planes for cominuscule varieties such as Grassmannians. We also show that the singular locus of the secant varieties $\sigma_r(Seg(\mathbb P^n\times\mathbb P^m\times \mathbb P^q))$ has codimension at least two for $r=2,3$.
Classification : 14M17
Keywords: tensor rank, secant varieties 
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     title = {On the third secant variety},
     journal = {Journal of Algebraic Combinatorics},
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     year = {2014},
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Buczyński, Jarosław; Landsberg, J.M. On the third secant variety. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 2, pp. 475-502. http://geodesic.mathdoc.fr/item/JAC_2014__40_2_a5/