English

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.

Keywords

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}
}
R2 v1 2026-06-28T17:26:46.383Z