Gorenstein sequences of high socle degrees
J. Korean Math. Soc. 2022 Vol. 59, No. 1, 71-85
https://doi.org/10.4134/JKMS.j200690
Published online October 29, 2021
Printed January 1, 2022
Jung Pil Park, Yong-Su Shin
Seoul National University; Sungshin Women's University
Abstract : In \cite{AS:3}, the authors showed that if an $h$-vector $(h_0,h_1,\dots,h_e)$ with $h_1=4e-4$ and $h_i\le h_1$ is a Gorenstein sequence, then $h_1=h_i$ for every $1\le i\le e-1$ and $e\ge 6$. In this paper, we show that if an $h$-vector $(h_0,h_1,\dots,h_e)$ with $h_1=4e-4$, $h_2=4e-3$, and $h_i\le h_2$ is a Gorenstein sequence, then $h_2=h_i$ for every $2\le i\le e-2$ and $e\ge 7$. We also propose an open question that if an $h$-vector $(h_0,h_1,\dots,h_e)$ with $h_1=4e-4$, $4e-3
Keywords : Gorenstein $h$-vectors, unimodal or nonunimodal $h$-vectors, Hilbert functions
MSC numbers : Primary 13D40; Secondary 13H10, 14C20
Supported by : This research was supported by a grant from Sungshin Women's University.
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