The minimal free resolution of a generic symmetric principal ideal
Commutative Algebra
2024-09-05 v2
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 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.
Keywords
Cite
@article{arxiv.2308.03141,
title = {The minimal free resolution of a generic symmetric principal ideal},
author = {Megumi Harada and Alexandra Seceleanu and Liana Şega},
journal= {arXiv preprint arXiv:2308.03141},
year = {2024}
}
Comments
to appear in Transactions of the AMS