Diagonal F-Thresholds on Binomial Hypersurfaces

Abstract

In this article, we study the diagonal F-threshold, that is, the F-threshold of the maximal ideal with respect to the maximal ideal itself. In particular, we give a formula of the diagonal F-thresholds for binomial hypersurfaces, and compare the diagonal F-thresholds with F-pure thresholds for strongly F-regular binomial hypersurfaces.

As a result, we prove that those diagonal F-thresholds always exist and they are rational numbers in that case.

Key Words:

• Binomial hypersurface
• F-pure threshold
• F-threshold
• Strongly F-regular

2000 Mathematics Subject Classification:

• Primary 13A35
• Secondary 13H10

ACKNOWLEDGMENT

The authors wish to thank Professor Kei-ichi Watanabe for many valuable comments. Also, the authors thank the referee for many valuable comments.

Notes

Communicated by S. Goto.