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Structure theorems for Gorenstein ideals of codimension four with small number of generators

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arxiv 2503.08813 v1 pith:BVP52CWR submitted 2025-03-11 math.AC

Tymoteusz Chmiel , Lorenzo Guerrieri , Xianglong Ni , Jerzy Weyman This is my paper · ORCID
classification math.AC
keywords codimensiongorensteinfouridealselementsgeneratedidealminimally
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Restrictions on the Betti tables of licci ideals

    math.AC 2026-08 conditional novelty 6.0 of 10

    For several large classes of licci ideals, the number of generators is bounded by the largest shift in the last step of the graded free resolution, confirming part of three new conjectures.

  2. Generic models of licci ideals parametrized by Schur functors

    math.AC 2025-06 conditional novelty 6.0 of 10

    Herzog classes of codimension-3 licci ideals are parametrized by pairs of partitions via a graph of direct links, with applications to Tor algebra structures.

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