2 citations · 4 across the 15 of their papers we have counts for
16 papers
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…
Some Taylor varieties with null Hessian
Thais Gomes Ribeiro, Elena Guardo, Manuela Muzika Dizdarević +3
Taylor varieties arise from Taylor expansion of rational functions in variables. Among them, we look for non-defective hypersurfaces. We prove that the…
On the strong base locus of a projective variety
Edoardo Ballico, Maria Chiara Brambilla, Pierpaola Santarsiero
We introduce and study the base locus and the strong base locus of a projective variety X. The base locus of X parametrizes configurations of smooth points of X where the span of t…
A new bound on the rank of tensor product of W-states
S. Canino, A. Casarotti, P. Santarsiero
A W-state is an order d symmetric tensor of the form W_d=x^{d-1}y. We prove that the partially symmetric rank of W_{d_1}\otimes \cdots \otimes W_{d_k} is at most 2^{k-1}(d_1+\cdots…
Path signatures of ODE solutions
Francesco Galuppi, Giovanni Moreno, Pierpaola Santarsiero
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. By employing the geometric theory of nonlinear systems of ordinary differential equa…
Computation of dominant ideals
Anna Maria Bigatti, Nursel Erey, Selvi Kara +4
We consider the problem of determining whether a monomial ideal is dominant. This property is critical for determining for which monomial ideals the Taylor resolution is minimal. W…
Rank and symmetries of signature tensors
Francesco Galuppi, Pierpaola Santarsiero
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. In this paper we propose a systematic study of basic properties of signature tensors…
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…
Degree of the subspace variety
Paul Breiding, Pierpaola Santarsiero
Subspace varieties are algebraic varieties whose elements are tensors with bounded multilinear rank. In this paper, we compute their degrees by computing their volumes.
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…
Decomposing Tensor Spaces via Path Signatures
Carlos Améndola, Francesco Galuppi, Ángel David Ríos Ortiz +2
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors…
The symmetric geometric rank of symmetric tensors
Julia Lindberg, Pierpaola Santarsiero
Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of the symmetric geometric rank of a symm…
Average degree of the essential variety
Paul Breiding, Samantha Fairchild, Pierpaola Santarsiero +1
The essential variety is an algebraic subvariety of dimension in real projective space which encodes the relative pose of two calibrated pinhole camera…
An algorithm for the non-identifiability of rank-3 tensors
Pierpaola Santarsiero
We present an algorithm aimed to recognize if a given tensor is a non-identifiable rank-3 tensor.
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…