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Proceedings of the American Mathematical Society

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

 

 

A note on complete intersections
of height three


Author: Junzo Watanabe
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
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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
Email: junzowat@ss.u-tokai.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-98-04477-3
Keywords: Homogeneous Artinian algebra, complete intersection, weak Lefschetz condition
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
Article copyright: © Copyright 1998 American Mathematical Society