Diagonal F-thresholds and F-pure thresholds of Hibi rings

TL;DR

This paper computes diagonal F-thresholds and F-pure thresholds for Hibi rings, a class of graded toric rings associated with finite distributive lattices, advancing understanding of their algebraic properties in positive characteristic.

Contribution

It provides explicit calculations of F-thresholds and F-pure thresholds for Hibi rings, a novel contribution to the study of their singularities and Frobenius invariants.

Findings

Explicit formulas for diagonal F-thresholds of Hibi rings

Explicit formulas for F-pure thresholds of Hibi rings

Enhanced understanding of Frobenius invariants in toric rings

Abstract

Hibi rings are a kind of graded toric ring on a finite distributive lattice $D = J(P)$, where $P$ is a partially ordered set. In this paper, we compute diagonal F-thresholds and F-pure thresholds of Hibi rings.