The minimal free resolution of a general principal symmetric ideal

Harada, Megumi; Seceleanu, Alexandra; Şega, Liana

doi:10.1090/tran/9314

The minimal free resolution of a general principal symmetric ideal
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by Megumi Harada, Alexandra Seceleanu and Liana M. Şega;

Trans. Amer. Math. Soc. 378 (2025), 1831-1882

DOI: https://doi.org/10.1090/tran/9314

Published electronically: December 30, 2024

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Abstract:

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 non-empty 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.

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