Diagonal F-thresholds and F-pure Thresholds of Hibi 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 and give a characterization of Hibi rings which satisfy the equality between these invariants in terms of its trivialness in the sense of Herzog–Hibi–Restuccia.

Key Words:

• A-invariant
• F-threshold
• F-pure threshold
• Hibi ring

2010 Mathematics Subject Classification:

• Primary: 13A35
• Secondary: 05E40

ACKNOWLEDGMENT

First of all, the authors wish to thank Professor Ken-ichi Yoshida for many valuable comments and his encouragement. They also indebted to Professor Kei-ichi Watanabe for his valuable suggestions about Question 4.4. Moreover, they would like to thank Professor Mitsuyasu Hashimoto for his indication about our mistake of the proof of Theorem 2.4. Finally, they would like to thank the referees for their careful reading of this article.

Notes

Communicated by I. Swanson.