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http://dx.doi.org/10.4134/JKMS.j200690

GORENSTEIN SEQUENCES OF HIGH SOCLE DEGREES  

Park, Jung Pil (Faculty of Liberal Education Seoul National University)
Shin, Yong-Su (Department of Mathematics Sungshin Women's University)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.1, 2022 , pp. 71-85 More about this Journal
Abstract
In [4], the authors showed that if an h-vector (h0, h1, …, he) with h1 = 4e - 4 and hi ≤ h1 is a Gorenstein sequence, then h1 = hi for every 1 ≤ i ≤ e - 1 and e ≥ 6. In this paper, we show that if an h-vector (h0, h1, …, he) with h1 = 4e - 4, h2 = 4e - 3, and hi ≤ h2 is a Gorenstein sequence, then h2 = hi for every 2 ≤ i ≤ e - 2 and e ≥ 7. We also propose an open question that if an h-vector (h0, h1, …, he) with h1 = 4e - 4, 4e - 3 < h2 ≤ (h1)(1)|+1+1, and h2 ≤ hi is a Gorenstein sequence, then h2 = hi for every 2 ≤ i ≤ e - 2 and e ≥ 6.
Keywords
Gorenstein h-vectors; unimodal or nonunimodal h-vectors; Hilbert functions;
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