5 papers · 1 filter
On Waring rank jumps via critical rank-one approximations
Alessandro Oneto, Pierpaola Santarsiero, Ettore Teixeira Turatti
We investigate whether eigenvectors, also known as critical rank-one approximations, of a symmetric tensor can be used to increase or decrease its Waring rank. First, we study the…
Finiteness of Hadamard ranks
Dario Antolini, Edoardo Ballico, Alessandro Oneto
The Hadamard rank of a point with respect to a projective variety is, if it exists, the minimum number of points of the variety whose coordinate-wise product is the given point. We…
Polynomials of small slice rank and strength
Cosimo Flavi, Fulvio Gesmundo, Alessandro Oneto +1
This paper investigates defining equations for secant varieties of the variety of reducible polynomials, which geometrically encode the notions of strength and slice rank of homoge…
Postulation for 2-superfat points in the plane
Stefano Canino, Maria Virginia Catalisano, Alessandro Gimigliano +2
We study the postulation of 0-dimensional schemes given by unions of 2-superfat points in general position in the plane, i.e., the union of local schemes defined by the intersectio…
Decomposition loci of tensors
Alessandra Bernardi, Alessandro Oneto, Pierpaola Santarsiero
The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of an…