Trimming a Gorenstein ideal

Abstract

Let Q be a regular local ring of dimension 3. We show how to trim a Gorenstein ideal in Q to obtain an ideal that defines a quotient ring that is close to Gorenstein in the sense that its Koszul homology algebra is a Poincare duality algebra P padded with a non-zero graded vector space on which P_{\ge 1} acts trivially. We explicitly construct an infinite family of such rings.

Corrected statement of Lemma 2.3 and updated proof of Theorem 2.4. Final version, to appear in J. Commut. Algebra; 11 pp