2025/03/11 by Tymoteusz Chmiel, Chmiel, Tymoteusz, Lorenzo Guerrieri +5
Mathematics · #13C05 #13D02 #13H10 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2503.08813
openalex publication_date 2025/03/11 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28
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.