5 citations · 5 across the 8 of their papers we have counts for
11 papers
On the unirationality of conic bundles with discriminant of degree eight
Alex Casarotti, Søren Gammelgaard, Alex Massarenti
We study the unirationality of surface conic bundles over an arbitrary field with discriminant degree , the first case beyond the del Pezzo ran…
On defectivity of joins, reducible secants and Fröberg's conjecture
Alexander Blomenhofer, Alex Casarotti
We introduce the notion of r-defectivity for a vector bundle on a quasi-projective variety. Using this tool, we prove several previously unknown cases of Fröberg's conjecture and a…
Nondefectivity of invariant secant varieties
Alexander Taveira Blomenhofer, Alex Casarotti
We show that a large class of secant varieties is nondefective. In particular, we positively resolve most cases of the Baur-Draisma-de Graaf conjecture on Grassmannian secants in l…
Waring identifiability for powers of forms via degenerations
Alex Casarotti, Elisa Postinghel
We discuss an approach to the secant non-defectivity of the varieties parametrizing -th powers of forms of degree . It employs a Terracini type argument along with certain de…
Identifiability for mixtures of centered Gaussians and sums of powers of quadratics
Alexander Taveira Blomenhofer, Alex Casarotti, Alessandro Oneto +1
We consider the inverse problem for the polynomial map which sends an -tuple of quadratic forms in variables to the sum of their -th powers. This map captures the moment…
Complete singular collineations and quadrics
Alex Casarotti, Elsa Corniani, Alex Massarenti
We construct wonderful compactifications of the spaces of linear maps, and symmetric linear maps of a given rank as blow-ups of secant varieties of Segre and Veronese varieties. Fu…
Tangential weak defectiveness and generic identifiability
Alex Casarotti, Massimiliano Mella
We investigate the uniqueness of decomposition of general tensors as a sum of tensors of rank . This is done ex…
On tangential weak defectiveness and identifiability of projective varieties
Ageu Barbosa Freire, Alex Casarotti, Alex Massarenti
A point of a projective space is -identifiable, with respect to a variety , if it can be written as linear combination of elements o…
On secant dimensions and identifiability of Flag varieties
Ageu Barbosa Freire, Alex Casarotti, Alex Massarenti
We investigate the secant dimensions and the identifiablity of flag varieties parametrizing flag of sub vector spaces of a fixed vector space. We give numerical conditions ensuring…
From non Defectivity to Identifiability
Alex Casarotti, Massimiliano Mella
A projective variety is -identifiable if the generic element in its -secant variety uniquely determines points on . In this paper we propose an…
On Comon's and Strassen's conjectures
Alex Casarotti, Alex Massarenti, Massimiliano Mella
Comon's conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen's conjecture on the additivity of the rank of tensors are two of the most…