61 citations · 61 across the 4 of their papers we have counts for
9 papers · 1 filter
The normal map for plane curves and pathologies in positive characteristic
Edoardo Ballico, Alessandro Oneto
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…
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,…
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…
Border Waring Rank via Asymptotic Rank
Matthias Christandl, Fulvio Gesmundo, Alessandro Oneto
We investigate an extension of a lower bound on the Waring (cactus) rank of homogeneous forms due to Ranestad and Schreyer. We show that for particular classes of homogeneous forms…
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…
The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
Alessandra Bernardi, Enrico Carlini, Maria Virginia Catalisano +2
We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety . The case we concentrate on is when i…