A note on complete intersections of height three

Watanabe, Junzo

doi:10.1090/S0002-9939-98-04477-3

A note on complete intersections of height three
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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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