Linkage classes of grade 3 perfect ideals

Abstract

While every grade 2 perfect ideal in a regular local ring is linked to a complete intersection ideal, it is known not to be the case for ideals of grade 3. We soften the blow by proving that every grade 3 perfect ideal in a regular local ring is linked to a complete intersection or a Golod ideal. Our proof is indebted to a homological classification of Cohen-Macaulay local rings of codimension 3. That debt is swiftly repaid, as we use linkage to reveal some of the finer structures of this classification.

Added proofs of 4.1 and 4.4; strengthened 5.3. Final version, to appear in J. Pure Appl. Algebra; 29 pp