Structure theorems for Gorenstein ideals of codimension four with small number of generators
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910870427140096 |
|---|---|
| author | Chmiel, Tymoteusz Guerrieri, Lorenzo Ni, Xianglong Weyman, Jerzy |
| author_facet | Chmiel, Tymoteusz Guerrieri, Lorenzo Ni, Xianglong Weyman, Jerzy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure theorems for Gorenstein ideals of codimension four with small number of generators Chmiel, Tymoteusz Guerrieri, Lorenzo Ni, Xianglong Weyman, Jerzy Commutative Algebra 13C05, 13D02, 13H10 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. |
| title | Structure theorems for Gorenstein ideals of codimension four with small number of generators |
| topic | Commutative Algebra 13C05, 13D02, 13H10 |
| url | https://arxiv.org/abs/2503.08813 |