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arXiv · 1211.7306

On polynomials with given Hilbert function and applications

Alessandra Bernardi·Joachim Jelisiejew·Pedro Macias Marques·Kristian Ranestad
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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.

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Alessandra Bernardi, Joachim Jelisiejew, Pedro Macias Marques, Kristian Ranestad. 2016-06-23. On polynomials with given Hilbert function and applications. https://doi.org/10.1007/s13348-016-0190-2

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