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…