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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.

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A note on complete intersections of height three
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by Junzo Watanabe PDF
Proc. Amer. Math. Soc. 126 (1998), 3161-3168 Request permission

Abstract:

Let $k$ be a field of characteristic 0. If $I \subset k[x,y,z]$ is a complete intersection generated by three homogeneous elements of degrees $d_1,d_2,d_3$ with $2 \le d_1 \le d_2 \le d_3$, then the reduction of $I$ by a general linear form is minimally generated by three elements if and only if $d_3 \le d_1+d_2-2$.
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Additional Information
  • Junzo Watanabe
  • MR Author ID: 243001
  • Email: junzowat@ss.u-tokai.ac.jp
  • Received by editor(s): July 11, 1996
  • Received by editor(s) in revised form: March 28, 1997
  • Additional Notes: This research was supported by Project C of Tokai University.
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3161-3168
  • MSC (1991): Primary 13H05
  • DOI: https://doi.org/10.1090/S0002-9939-98-04477-3
  • MathSciNet review: 1459155