An ADE correspondence for grade three perfect ideals
Abstract
Using the theory of "higher structure maps" from generic rings for free resolutions of length three, we give a classification of grade 3 perfect ideals with small type and deviation in local rings of equicharacteristic zero, extending the Buchsbaum-Eisenbud structure theorem on Gorenstein ideals and realizing it as the type D case of an ADE correspondence. We also deduce restrictions on Betti tables in the graded setting for such ideals.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.02380
- arXiv:
- arXiv:2407.02380
- Bibcode:
- 2024arXiv240702380G
- Keywords:
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- Mathematics - Commutative Algebra;
- 13C05