Linkage classes of grade 3 perfect ideals

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Christensen, Lars Winther¹  Veliche, Oana²  Weyman, Jerzy³ 

[1] Texas Tech Univ, Lubbock, TX 79409 USA

[2] Northeastern Univ, Boston, MA 02115 USA

[3] Univ Connecticut, Storrs, CT 06269 USA

关键词: Complete intersection;    Golod;    Linkage;    Local ring;    Tor algebra;   

DOI  :  10.1016/j.jpaa.2019.07.007

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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