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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 | References | Similar Articles | Additional Information

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 $d_3 \le d_1+d_2-2$.


References [Enhancements On Off] (What's this?)

  • 1. D. A. Buchsbaum and D. Eisenbud, Algebraic structures for finite free resolutions, and some structure theorem for ideals of codimension 3, Amer. J. Math. 99 (1977), 447-485. MR 56:11983
  • 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
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

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