Herzog ideals and F-singularities
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.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Rings
Modules
and Algebras
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Volume
- 230
- Issue
- 11
- Pages
- 108404–108404
- Publication date
- 28 September 2026
- Language
- EN