Linkage classes of grade 3 perfect ideals
Commutative Algebra
2019-06-05 v2
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.
Cite
@article{arxiv.1812.11552,
title = {Linkage classes of grade 3 perfect ideals},
author = {Lars Winther Christensen and Oana Veliche and Jerzy Weyman},
journal= {arXiv preprint arXiv:1812.11552},
year = {2019}
}
Comments
Added proofs of 4.1 and 4.4; strengthened 5.3. Final version, to appear in J. Pure Appl. Algebra; 29 pp