Resumen de On polynomials with given Hilbert function and applications

Alessandra Bernardi, Joachim Jelisiejew, Pedro Macias Marques, Kristian Ranestad

• Using Macaulay’s correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.