6 citations · 10 across the 12 of their papers we have counts for
12 papers
On defective spans of singular vector tuples beyond the boundary format
Ettore Teixeira Turatti, Emanuele Ventura
In this paper, we study tensor spaces beyond the boundary format and analyze whether the general critical space coincides with the general span of singular vector tuples. For all t…
Weak and strong Lefschetz properties for Hartshorne-Rao modules of curves in
Juan Migliore, Uwe Nagel, Chris Peterson +1
Let be a curve over an algebraically closed field of characteristic zero, and let denote its Hartshorne-Rao module. We study how the geometry of i…
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…
Quadrature rules with few nodes supported on algebraic curves
Cordian Riener, Ettore Teixeira Turatti
We investigate quadrature rules for measures supported on real algebraic and rational curves, focusing on the {odd-degree} case \(2s-1\). Adopting an optimization viewpoint, we min…
Decomposing tensors via rank-one approximations
Alvaro Ribot, Emil Horobet, Anna Seigal +1
Matrices can be decomposed via rank-one approximations: the best rank-one approximation is a singular vector pair, and the singular value decomposition writes a matrix as a sum of…
Generalized identifiability of sums of squares
Giorgio Ottaviani, Ettore Teixeira Turatti
Let be a homogeneous polynomial of even degree . We study the decompositions where . The minimal number of summands is calle…
Geometry of first nonempty Terracini loci
Francesco Galuppi, Pierpaola Santarsiero, Douglas A. Torrance +1
After a few results on curves, we characterize the smallest nonempty Terracini loci of Veronese and Segre-Veronese varieties. For del Pezzo surfaces, we give a full description of…
Characteristic polynomials and eigenvalues of tensors
Francesco Galuppi, Fulvio Gesmundo, Ettore Teixeira Turatti +1
We lay the geometric foundations for the study of the characteristic polynomial of tensors. For symmetric tensors of order and dimension , and symmetric tensors of or…
When does subtracting a rank-one approximation decrease tensor rank?
Emil Horobet, Ettore Teixeira Turatti
Subtracting a critical rank-one approximation from a matrix always results in a matrix with a lower rank. This is not true for tensors in general. Motivated by this, we ask the que…
The span of singular tuples of a tensor beyond the boundary format
Luca Sodomaco, Ettore Teixeira Turatti
A singular -tuple of a tensor of format is essentially a complex critical point of the distance function from constrained to the cone of tensors of fo…
On the degree of varieties of sum of squares
Andrew Ferguson, Giorgio Ottaviani, Mohab Safey El Din +1
We study the problem of how many different sums of squares decompositions a general polynomial with SOS-rank admits. We show that there is a link between the variety $\math…
On tensors that are determined by their singular tuples
Ettore Teixeira Turatti
In this paper we study the locus of singular tuples of a complex valued multisymmetric tensor. The main problem that we focus on is: given the set of singular tuples of some genera…