Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the stable Harbourne conjecture for ideals defining space monomial curves
HTML articles powered by AMS MathViewer

by Kosuke Fukumuro and Yuki Irie PDF
Proc. Amer. Math. Soc. 151 (2023), 1445-1458 Request permission


For the ideal $\mathfrak {p}$ in $k[x, y, z]$ defining a space monomial curve, we show that $\mathfrak {p}^{(2 n - 1)} \subseteq \mathfrak {m} \mathfrak {p}^{n}$ for some positive integer $n$, where $\mathfrak {m}$ is the maximal ideal $(x, y, z)$. Moreover, the smallest such $n$ is determined. It turns out that there is a counterexample to a claim due to Grifo, Huneke, and Mukundan, which states that $\mathfrak {p}^{(3)} \subseteq \mathfrak {m} \mathfrak {p}^2$ if $k$ is a field of characteristic not $3$; however, the stable Harbourne conjecture holds for space monomial curves as they claimed.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 13A15, 13H05
  • Retrieve articles in all journals with MSC (2020): 13A15, 13H05
Additional Information
  • Kosuke Fukumuro
  • Affiliation: Department of Mathematics and Informatics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
  • MR Author ID: 1015594
  • ORCID: 0000-0001-6446-0661
  • Email:
  • Yuki Irie
  • Affiliation: Research Alliance Center for Mathematical Sciences, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8578, Japan
  • MR Author ID: 1287511
  • ORCID: 0000-0002-6034-656X
  • Email:,
  • Received by editor(s): April 22, 2022
  • Received by editor(s) in revised form: July 2, 2022
  • Published electronically: January 24, 2023
  • Additional Notes: The second author was partially supported by JSPS KAKENHI Grant Number JP20K14277.
    The second author is the corresponding author.

  • Dedicated: Dedicated to Professor Koji Nishida on the occasion of his sixtieth birthday
  • Communicated by: Claudia Polini
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 1445-1458
  • MSC (2020): Primary 13A15; Secondary 13H05
  • DOI: