Author:
Bezerra Lenin,Gondim Rodrigo,Ilardi Giovanna,Zappalà Giuseppe
Abstract
AbstractWe conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing codimension and length. We prove the conjecture in length four and five, in low codimension. We also prove the conjecture for a particular subclass of algebras that occurs in every length and certain codimensions. As a consequence of our methods we give a new proof of part of a known result about the asymptotic behavior of the minimum entry of a Gorenstein Hilbert function.
Funder
Università degli Studi di Napoli Federico II
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference21 articles.
1. Abdallah, N., Altafi, N., De Poi, P., Fiorindo, L., Iarrobino, A., Marques, P.M., Nicklasson, L.: Hilbert functions and Jordan type of Perazzo Artinian algebras (2023). arXiv preprint arXiv:2303.16768
2. Ahn, J., Migliore, J.C., Shin, Y.S.: Green’s theorem and Gorenstein sequences. J. Pure Appl. Algebra 222, 387–413 (2018)
3. Bernstein, D., Iarrobino, A.: A nonunimodal graded Gorenstein Artin algebra in codimension five. Commun. Algebra 20(8), 2323–2336 (1992)
4. Boij, M.: Graded Gorenstein Artin algebras whose Hilbert functions have a large number of valleys. Commun. Algebra 23(1), 97–103 (1995)
5. Boij, M., Laksov, D.: Nonunimodality of graded Gorenstein Artin algebras. Proc. Am. Math. Soc. 120(4), 1083–1092 (1994)
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1. Correction to the bibliography: On minimal Gorenstein Hilbert functions;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2024-06-04
2. Perazzo n-folds and the weak Lefschetz property;Rendiconti del Circolo Matematico di Palermo Series 2;2024-05-28