The first example of a non unimodal Gorenstein $h$-vector was given by Stanley, it is $(1,13,12,13,1)$. In cite{MZa} the authors showed that Stanley's example is optimal, {it i.e.}, the vector $(1,12,11,12,1)$ is not a Gorenstein $h$-vector. Our main result is a generalization of this result. We also give a simple proof of Stanley's conjecture on the asymptotic behavior of the Hilbert function in socle degree four. We present a conjecture about the asymptotic behaviour of the Hilbert function for those algebras that are presented by quadrics.
On the Hilbert function of Gorenstein algebras of socle degree four / Cerminara, Armando; Gondim, Rodrigo; Ilardi, Giovanna; Zappalà, Giuseppe. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 224, Issue 12, December 2020, Article number 106434:12(2020). [10.1016/j.jpaa.2020.106434]
On the Hilbert function of Gorenstein algebras of socle degree four
Armando Cerminara;Giovanna Ilardi
;
2020
Abstract
The first example of a non unimodal Gorenstein $h$-vector was given by Stanley, it is $(1,13,12,13,1)$. In cite{MZa} the authors showed that Stanley's example is optimal, {it i.e.}, the vector $(1,12,11,12,1)$ is not a Gorenstein $h$-vector. Our main result is a generalization of this result. We also give a simple proof of Stanley's conjecture on the asymptotic behavior of the Hilbert function in socle degree four. We present a conjecture about the asymptotic behaviour of the Hilbert function for those algebras that are presented by quadrics.| File | Dimensione | Formato | |
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