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
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Geometry
Lower bounds
Mathematics
Mathematics and Statistics
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Beschreibung
Zusammenfassung: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.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-016-0190-2