2023/08/06 by Megumi Harada, Harada, Megumi, Alexandra Seceleanu +3
Mathematics · #13D07 #20C30 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary: 13D02 primary. Secondary 13A50 #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2308.03141
openalex publication_date 2023/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is parametrized by points in a suitable projective space. We show that the minimal free resolution of a principal symmetric ideal is constant on a nonempty Zariski open subset of this projective space and we determine this resolution explicitly. Along the way, we study two classes of graded algebras which we term narrow and extremely narrow; both of which are instances of compressed artinian algebras.