On $F$-thresholds of differential power filtrations

Abstract

We study the $F$-threshold of differential power filtrations of monomial ideals. We give the existence of this number and show that it is upper bounded by the maximum height of the minimal primes of the underlying monomial ideal. As an application of our results, we show that the dimension of the polynomial ring and the $F$-threshold of the differential power filtration of the monomial maximal ideal are the same.