An ADE correspondence for grade three perfect ideals
Commutative Algebra
2024-07-03 v1
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.
Cite
@article{arxiv.2407.02380,
title = {An ADE correspondence for grade three perfect ideals},
author = {Lorenzo Guerrieri and Xianglong Ni and Jerzy Weyman},
journal= {arXiv preprint arXiv:2407.02380},
year = {2024}
}