On polynomials with given Hilbert function and applications

On polynomials with given Hilbert function and applications

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, whe...

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Veröffentlicht in:Collectanea mathematica (Barcelona) 2018, Vol.69 (1), p.39-64
Hauptverfasser: Bernardi, Alessandra, Jelisiejew, Joachim, Marques, Pedro Macias, Ranestad, Kristian
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Algebra
Analysis
Applications of Mathematics
Geometry
Lower bounds
Mathematics
Mathematics and Statistics
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container_title Collectanea mathematica (Barcelona)
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creator Bernardi, Alessandra
Jelisiejew, Joachim
Marques, Pedro Macias
Ranestad, Kristian
description 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.
doi_str_mv 10.1007/s13348-016-0190-2
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subjects Algebra
Analysis
Applications of Mathematics
Geometry
Lower bounds
Mathematics
Mathematics and Statistics
title On polynomials with given Hilbert function and applications
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