Work

Herzog ideals and F-singularities

Year: 2026

Type: article

Abstract: In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gröbner degeneration) and $F$-singularities. More precisely, we show that, in positive characteristic, homogeneous Herzog ideals define $F$-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 $F$-pure type.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2026.108404

Authors: Alessandro De Stefani, Linquan Ma, Matteo Varbaro

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550