On polynomials with given Hilbert function and applications

Abstract

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 cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

References in corpus (2)

• On the cactus rank of cubics forms
• Irreducibility of the Gorenstein loci of Hilbert schemes via ray families

Cited by in corpus (5)

• Partially symmetric variants of Comon's problem via simultaneous rank
• Waring, tangential and cactus decompositions
• A note on the cactus rank for Segre-Veronese varieties
• Symmetric Decomposition of the Associated Graded Algebra of an Artinian Gorenstein Algebra
• On schemes evinced by generalized additive decompositions and their regularity