Linkage classes of grade 3 perfect ideals

Lars Winther Christensen, Oana Veliche, Jerzy Weyman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Article number106185
JournalJournal of Pure and Applied Algebra
Volume224
Issue number6
DOIs
StatePublished - Jun 2020

Keywords

  • Complete intersection
  • Golod
  • Linkage
  • Local ring
  • Tor algebra

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