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.
2000 Mathematics Subject Classification:
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.