27 citations · 42 across the 10 of their papers we have counts for
10 papers
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…
Symmetric rank of some reducible forms
Liena Colarte-Gómez, Francesco Galuppi
In this paper, we study the symmetric rank of products of linear forms and an irreducible quadratic form. The main result presents a new, non-trivial lower bound for the rank, and…
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…
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…
Generic identifiability of pairs of ternary forms
Valentina Beorchia, Francesco Galuppi
We prove that two general ternary forms are simultaneously identifiable only in the classical cases of two quadratic and a cubic and a quadratic form. We translate the problem into…
Veronese and Segre morphisms between non-commutative projective spaces
Francesca Arici, Francesco Galuppi, Tatiana Gateva-Ivanova
We study Veronese and Segre morphisms between non-commutative projective spaces. We compute finite reduced Gröbner bases for their kernels, and we compare them with their analogues…
The Rough Veronese variety
Francesco Galuppi
We study signature tensors of paths from a geometric viewpoint. The signatures of a given class of paths parametrize an algebraic variety inside the space of tensors, and these sig…
On the unique unexpected quartic in
Łucja Farnik, Francesco Galuppi, Luca Sodomaco +1
The computation of the dimension of linear systems of plane curves through a bunch of given multiple points is one of the most classic issues in Algebraic Geometry. In general, it…
Identifiability of homogeneous polynomials and Cremona Transformations
Francesco Galuppi, Massimiliano Mella
A homogeneous polynomial of degree in variables is identifiable if it admits a unique additive decomposition in powers of linear forms. Identifiability is expected to be…