Structure theorems for Gorenstein ideals of codimension four with small number of generators
Commutative Algebra
2025-03-13 v1
Abstract
In this article we study minimal free resolutions of Gorenstein ideals of codimension four, using methods coming from representation theory. We introduce families of higher structure maps associated with such resolution, defined similarly to the codimension three case. As our main application, we prove that every Gorenstein ideal of codimension four minimally generated by six elements is a hyperplane section of a Gorenstein ideal of codimension three, strengthening a result by Herzog-Miller and Vasconcelos-Villarreal. We state analogous conjectural results for ideals minimally generated by seven and eight elements.
Cite
@article{arxiv.2503.08813,
title = {Structure theorems for Gorenstein ideals of codimension four with small number of generators},
author = {Tymoteusz Chmiel and Lorenzo Guerrieri and Xianglong Ni and Jerzy Weyman},
journal= {arXiv preprint arXiv:2503.08813},
year = {2025}
}