19 citations · 113 across the 23 of their papers we have counts for
10 papers · 1 filter
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…
Tensors with maximal symmetries
Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +1
We classify tensors with maximal and next to maximal dimensional symmetry groups under a natural genericity assumption (1-genericity), in dimensions greater than 7. In other words,…
Rank and border rank of Kronecker powers of tensors and Strassen's laser method
Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +1
We prove that the border rank of the Kronecker square of the little Coppersmith-Winograd tensor is the square of its border rank for and that the border rank of…
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…
Strict inclusions of high rank loci
Edoardo Ballico, Alessandra Bernardi, Emanuele Ventura
For a given projective variety , the high rank loci are the closures of the sets of points whose -rank is higher than the generic one. We show examples of strict inclusion be…
Minimal degree equations for curves and surfaces (variations on a theme of Halphen)
Edoardo Ballico, Emanuele Ventura
Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree.…
Singular Curves of Low Degree and Multifiltrations from Osculating Spaces
Jarosław Buczyński, Nathan Ilten, Emanuele Ventura
In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occu…
The monic rank
Arthur Bik, Jan Draisma, Alessandro Oneto +1
We introduce the monic rank of a vector relative to an affine-hyperplane section of an irreducible Zariski-closed affine cone . We show that the monic rank is finite and greater…