Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2020.12.24
  • Accepted : 2021.08.04
  • Published : 2022.01.01
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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

Acknowledgement

This research was supported by a grant from Sungshin Women's University.

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