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A note on complete intersections of height three

Author(s): Junzo Watanabe
Journal: Proc. Amer. Math. Soc. 126 (1998), 3161-3168.
MSC (1991): Primary 13H05
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Abstract: Let be a field of characteristic 0. If $I \subset k[x,y,z]$ is a complete intersection generated by three homogeneous elements of degrees with $2 \le d_1 \le d_2 \le d_3$ , then the reduction of by a general linear form is minimally generated by three elements if and only if $d_3 \le d_1+d_2-2$ .

References:

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2.: J. H. Grace and A. Young, The algebra of invariants, Cambridge Univ. Press, 1903.
3.: A. Iarrobino, Associated graded algebra of a Gorenstein algebra, Mem. Amer. Math. Soc. 107 1994. MR 94f:13009
4.: -, Compressed algebras, Trans. Amer. Math. Soc. 285 (1984), 337-378. MR 85j:13030
5.: J. Watanabe, The Dilworth number of Artinian rings and finite posets with rank function, Adv. Stud. Pure Math. 11 (1987), 303-312. MR 89k:13015
6.: -, $\mathfrak{m}$ -Full ideals, Nagoya Math. J. 106 (1987), 101-111. MR 88g:13003
7.: -, A note on Gorenstein rings of embedding codimension three, Nagoya Math. J. 50 (1973), 227-232.

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Additional Information:

Junzo Watanabe
Affiliation: Department of Mathematical Sciences, Tokai University, Hiratsuka 259-1292, Japan
Email: junzowat@ss.u-tokai.ac.jp

DOI: 10.1090/S0002-9939-98-04477-3
PII: S 0002-9939(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
Copyright of article: Copyright 1998, American Mathematical Society


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