8 mar 2023 -- 11:30
Aula Tricerri, DIMaI, Firenze
Seminario di Geometria del Dini
Abstract.
The decompositions of polynomials, also known as Waring decompositions, have been widely studied in the literature. The determination of the Waring rank of a polynomial, that is the minimum number of powers of linear forms spanning the polynomial, despite being classical, is quite difficult, since at the present time, there is no explicit method to obtain it. In this work, we focus on powers of quadratic forms, of which many examples of decompositions appeared in the classical literature, especially for the real case. Our purpose is to deal with this problem from a modern point of view, with the final aim of determining its rank. The main tool we use is the apolarity lemma, by which it is possible to determine suitable decompositions of a given form.