Herzog ideals and $F$-singularities
Commutative Algebra
2026-01-13 v1 Algebraic Geometry
Abstract
In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gr\"obner degeneration) and -singularities. More precisely, we show that, in positive characteristic, homogeneous Herzog ideals define -anti-nilpotent rings, and we inquire, in characteristic 0, on a surprising relationship between being Herzog ideals after a change of coordinates and defining rings of dense open -pure type.
Keywords
Cite
@article{arxiv.2601.06476,
title = {Herzog ideals and $F$-singularities},
author = {Alessandro De Stefani and Linquan Ma and Matteo Varbaro},
journal= {arXiv preprint arXiv:2601.06476},
year = {2026}
}