Bounds on the F-Pure Threshold of Isolated Hypersurface Singularities

In this note, we obtain bounds for the $F$-pure threshold of isolated hypersurface singularities over an algebraically closed field of positive characteristic in terms of classical singularity invariants, notably the Milnor and Tjurina numbers. For curve singularities, we show that the $F$-pure threshold admits bounds, and often explicit computations, in terms of the generators of the associated value semigroup, yielding a positive-characteristic analogue of Igusa's formula for the log canonical threshold. As applications, we derive bounds on the log canonical threshold and the Briancon-Skoda exponent of complex isolated hypersurface singularities.