61 citations · 70 across the 5 of their papers we have counts for
14 papers
Terracini locus for three points on a Segre variety
Edoardo Ballico, Alessandra Bernardi, Pierpaola Santarsiero
We introduce the notion of r-th Terracini locus of a variety and we compute it for at most three points on a Segre variety.
Identifiability of rank-3 tensors
Edoardo Ballico, Alessandra Bernardi, Pierpaola Santarsiero
Rank-2 and rank-3 tensors are almost all identifiable with only few exceptions. We classify them all together with the dimensions and the structures of all the sets evincing the ra…
High Order Singular Value Decomposition for Plant Biodiversity Estimation
Alessandra Bernardi, Martina Iannacito, Duccio Rocchini
We propose a new method to estimate plant biodiversity with R{é}nyi and Rao indexes through the so called High Order Singular Value Decomposition (HOSVD) of tensors. Starting from…
Geometric conditions for strict submultiplicativity of rank and border rank
Edoardo Ballico, Alessandra Bernardi, Fulvio Gesmundo +2
The -rank of a point in projective space is the minimal number of points of an algebraic variety whose linear span contains . This notion is naturally submultiplicati…
Strict inclusions of high rank loci
Edoardo Ballico, Alessandra Bernardi, Emanuele Ventura
For a given projective variety , the high rank loci are the closures of the sets of points whose -rank is higher than the generic one. We show examples of strict inclusion be…
The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
Alessandra Bernardi, Enrico Carlini, Maria Virginia Catalisano +2
We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety . The case we concentrate on is when i…