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.
Free resolutions for principal symmetric ideals
Alexandra Seceleanu, University of Nebraska-LincolnAuthors: Megumi Harada, Alexandra Seceleanu, and Liana Sega
2023 AWM Research Symposium
Combinatorial and Homological Methods in Commutative Algebra [Organized by Francesca Gandini and Selvi Kara]