Castelnuovo-Mumford regularity up to symmetry
Commutative Algebra
2020-09-09 v3
Abstract
We study the asymptotic behavior of the Castelnuovo-Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of symmetric groups. A linear upper bound for the regularity of such ideals is established. We conjecture that their regularity grows eventually precisely linearly. We establish this conjecture in several cases, most notably when the ideals are Artinian or squarefree monomial.
Keywords
Cite
@article{arxiv.1806.00457,
title = {Castelnuovo-Mumford regularity up to symmetry},
author = {Dinh Van Le and Uwe Nagel and Hop D. Nguyen and Tim Roemer},
journal= {arXiv preprint arXiv:1806.00457},
year = {2020}
}
Comments
29 pages. Revised version, to appear in IMRN