13 papers
Strength and slice rank of forms are generically equal
Edoardo Ballico, Arthur Bik, Alessandro Oneto +1
We prove that strength and slice rank of homogeneous polynomials of degree over an algebraically closed field of characteristic zero coincide generically. To show this,…
The strength for line bundles
Edoardo Ballico, Emanuele Ventura
We introduce the strength for sections of a line bundle on an algebraic variety. This generalizes the strength of homogeneous polynomials that has been recently introduced to resol…
Entry loci and ranks
Edoardo Ballico, Emanuele Ventura
We study entry loci of varieties and their irreducibility from the perspective of -ranks with respect to a projective variety . These loci are the closures of the points that…
Vanishing Hessian, wild forms and their border VSP
Hang Huang, Mateusz Michałek, Emanuele Ventura
Wild forms are homogeneous polynomials whose smoothable rank is strictly larger than their border rank. The discrepancy between these two ranks is caused by the difference between…
Labels of real projective varieties
Edoardo Ballico, Emanuele Ventura
Let be a complex projective variety defined over . Recently, Bernardi and the first author introduced the notion of admissible rank with respect to . This rank ta…
Geometric conditions for strict submultiplicativity of rank and border rank
Edoardo Ballico, Alessandra Bernardi, Fulvio Gesmundo +2
The -rank of a point in projective space is the minimal number of points of an algebraic variety whose linear span contains . This notion is naturally submultiplicati…