A. Bernardi

activity

20072026

most citedComputing symmetric rank for symmetric tensors

205 citations · 676 across the 36 of their papers we have counts for

collaborators

Showing 2011 · math.AGShow all

5 papers · 2 filters

math.AG2011★ 11 cited

Grassmann secants, identifiability, and linear systems of tensors

Edoardo Ballico, Alessandra Bernardi, Maria Virginia Catalisano +1

For any irreducible non-degenerate variety $X \subset P^{r}$ , we give a criterion for the $(k, s)$ -identifiability of $X$ . If $k \leq s - 1 < r$ , then the $(k, s)$ -identifiability…

math.AG2011★ 53 cited

On the cactus rank of cubics forms

Alessandra Bernardi, Kristian Ranestad

We prove that the smallest degree of an apolar 0-dimensional scheme of a general cubic form in $n + 1$ variables is at most $2 n + 2$ , when $n \geq 8$ , and therefore smaller than the ran…

math.AG2011★ 49 cited

General Tensor Decomposition, Moment Matrices and Applications

Alessandra Bernardi, Jerome Brachat, Pierre Comon +1

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous t…

math.AG2011★ 18 cited

Higher secant varieties of $P^{n} \times P^{1}$ embedded in bi-degree $(a, b)$

Edoardo Ballico, Alessandra Bernardi, Maria Virginia Catalisano

In this paper we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of $P^{n} \times P^{1}$ via the section of the sheaf $\mathca…

math.AG2011★ 5 cited

Symmetric tensor rank with a tangent vector: a generic uniqueness theorem

Edoardo Ballico, Alessandra Bernardi

Let $X_{m, d} \subset P^{N}$ , $N := (m m + d) - 1$ , be the order $d$ Veronese embedding of $P^{m}$ . Let $τ (X_{m, d}) \subset P^{N}$ , be the tangent developabl…

Grassmann secants, identifiability, and linear systems of tensors

On the cactus rank of cubics forms

General Tensor Decomposition, Moment Matrices and Applications

Higher secant varieties of Pn×P1 embedded in bi-degree (a,b)

Symmetric tensor rank with a tangent vector: a generic uniqueness theorem

Higher secant varieties of $P^{n} \times P^{1}$ embedded in bi-degree $(a, b)$