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Isotropic Rank of Harmonic Polynomials
S. Canino, C. Flavi
Any homogeneous harmonic polynomial can be decomposed as a sum of powers of isotropic linear forms, that is, linear forms whose coefficients are the coordinates of isotropic points…
Polynomials of small slice rank and strength
Cosimo Flavi, Fulvio Gesmundo, Alessandro Oneto +1
This paper investigates defining equations for secant varieties of the variety of reducible polynomials, which geometrically encode the notions of strength and slice rank of homoge…
On the construction of a counterexample to Strassen's rank additivity conjecture
Viktoriia Borovik, Cosimo Flavi, Paweł Pielasa +2
The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individu…
Decompositions of powers of quadrics
Cosimo Flavi
We analyze the problem of determining Waring decompositions of the powers of any quadratic form over the field of complex numbers. Our main goal is to provide information about the…