4 papers
Border rank lower bounds beyond weak border apolarity
Tomasz Mańdziuk
We provide first examples of border rank lower bounds obtained using border apolarity beyond ``weak border apolarity''. Border apolarity introduced by Buczyńska-Buczyński character…
Symmetrization maps and minimal border rank Comon's conjecture
Tomasz Mańdziuk, Emanuele Ventura
One of the fundamental open problems in the field of tensors is the border Comon's conjecture: given a symmetric tensor for , its border a…
Tensoring by a plane maintains secant-regularity in degree at least two
Edoardo Ballico, Alessandra Bernardi, Tomasz Mańdziuk
Starting from an integral projective variety equipped with a very ample, non-special and not-secant defective line bundle , the paper establishes, under certain co…
Border apolarity and varieties of sums of powers
Tomasz Mańdziuk, Emanuele Ventura
We study border varieties of sums of powers ('s for short), recently introduced by Buczyńska and Buczyński, parameterizing border rank decompositions of a…