Grassmann secants and linear systems of tensors

Edoardo Ballico (1) , Alessandra Bernardi (2) , Maria Virgina Catalisano (3) , Luca Chiantini (4)

1 UNITN - Università degli Studi di Trento = University of Trento
2 GALAAD - Geometry, algebra, algorithms
3 DIPTEM - Dipartimento di Ingegneria della produzione, termoenergetica e modelli matematici
4 DSMI - Department of Mathematics and Computer Science / Dipartimento di Scienze Matematiche e Informatiche "Roberto Magari"

For any irreducible non-degenerate variety $X \subset \mathbb{P}^r$ , we relate the dimension of the $s$-th secant varieties of the Segre embedding of $\mathbb{P}^k\times X$ to the dimension of the $(k,s)$-Grassmann secant variety $GS_X(k,s)$ of $X$. We also give a criterion for the $s$-identifiability of $X$.

Domaines: Géométrie algébrique [math.AG]

Edoardo Ballico, Alessandra Bernardi, Maria Virgina Catalisano, Luca Chiantini. Grassmann secants and linear systems of tensors. Linear Algebra and its Applications, 2013, 438, pp.121-135. ⟨10.1016/j.laa.2012.07.045⟩. ⟨inria-00637780⟩