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.
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