F-invariants of diagonal hypersurfaces

TL;DR

This paper derives formulas for the F-pure threshold and test ideal of diagonal hypersurfaces over fields of prime characteristic, providing insights into their singularity structure and higher jumping numbers.

Contribution

It introduces explicit formulas for F-invariants of diagonal hypersurfaces and computes associated test ideals and higher jumping numbers, advancing understanding of their singularities.

Findings

Explicit formula for F-pure threshold of diagonal hypersurfaces

Calculation of test ideals at the F-pure threshold

Formulas for higher jumping numbers of Fermat hypersurfaces

Abstract

In this note, we derive a formula for the F-pure threshold of diagonal hypersurfaces over a perfect field of prime characteristic. We also calculate the associated test ideal at the F-pure threshold, and give formulas for higher jumping numbers of Fermat hypersurfaces.