Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Oneto, Alessandro"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G4, Pp 371-380 (2022)
The strength of a homogeneous polynomial (or form) is the smallest length of an additive decomposition expressing it whose summands are reducible forms. Using polynomial functors, we show that the set of forms with bounded strength is not always Zari
Externí odkaz:
https://doaj.org/article/1aba70f15a3b4c35ac3b48ae9ea5296f
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 any Segre variety, but not on the variety itself, we show that the decom
Externí odkaz:
http://arxiv.org/abs/2407.18138
We prove that Segre-Veronese varieties are never secant defective if each degree is at least three. The proof is by induction on the number of factors, degree and dimension. As a corollary, we give an almost optimal non-defectivity result for Segre-V
Externí odkaz:
http://arxiv.org/abs/2406.20057
Publikováno v:
Journal de Math\'ematiques Pures et Appliqu\'ees 188, 2024, pp. 446-469
We define and explicitly construct schemes evinced by generalized additive decompositions (GADs) of a given $d$-homogeneous polynomial $F$. We employ GADs to investigate the regularity of $0$-dimensional schemes apolar to $F$, focusing on those satis
Externí odkaz:
http://arxiv.org/abs/2309.12961
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise from statisti
Externí odkaz:
http://arxiv.org/abs/2308.06597
We prove the existence of ternary forms admitting apolar sets of points of cardinality equal to the Waring rank, but having different Hilbert function and different regularity. This is done exploiting liaison theory and Cayley-Bacharach properties fo
Externí odkaz:
http://arxiv.org/abs/2303.06780
We consider the inverse problem for the polynomial map which sends an $m$-tuple of quadratic forms in $n$ variables to the sum of their $d$-th powers. This map captures the moment problem for mixtures of $m$ centered $n$-variate Gaussians. In the fir
Externí odkaz:
http://arxiv.org/abs/2204.09356
Publikováno v:
In Journal de mathématiques pures et appliquées August 2024 188:446-469
Autor:
Ballico, Edoardo, Oneto, Alessandro
We study the normal map for plane projective curves, i.e., the map associating to every regular point of the curve the normal line at the point in the dual space. We first observe that the normal map is always birational and then we use this fact to
Externí odkaz:
http://arxiv.org/abs/2106.07426
Autor:
Galuppi, Francesco, Oneto, Alessandro
Publikováno v:
Advances in Mathematics, 409(B), 108657, 2022
Secant defectivity of projective varieties is classically approached via dimensions of linear systems with multiple base points in general position. The latter can be studied via degenerations. We exploit a technique that allows some of the base poin
Externí odkaz:
http://arxiv.org/abs/2104.02522