A note on primary powers of a prime ideal

Wei-Eihn Kuan

Vol. 108 (1983), No. 2, 319–325

DOI: 10.2140/pjm.1983.108.319

Abstract

Let X ⊂ P_kⁿ be an irreducible projective variety. Let B = k[x₀,…,x_n] and let P ⊂ B be the homogeneous prime ideal of X generated by ht(p) + 1 elements and let A = B∕P be the homogeneous coordinate ring of X. The following are equivalent: (1) A_(p) is a complete intersection for all homogeneous prime ideals p in A of height 1; (2) P² is primary: (3) Pⁱ is primary for all integers i > 0.

Mathematical Subject Classification 2000

Primary: 13A17, 13A17

Secondary: 13B30

Milestones

Received: 9 September 1980

Published: 1 October 1983