Linkage classes of grade 3 perfect ideals

Lars Winther Christensen; Oana Veliche; Jerzy Weyman

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arXiv · 1812.11552

Linkage classes of grade 3 perfect ideals

Lars Winther Christensen·Oana Veliche·Jerzy Weyman

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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.

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Lars Winther Christensen, Oana Veliche, Jerzy Weyman. 2019-06-04. Linkage classes of grade 3 perfect ideals. https://arxiv.org/abs/1812.11552

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