Relative projective curve/Behavior of Hilbert-Kunz slopes/Fact

Let

be a smooth projective relative curve and let be a vector bundle over . For the generic fiber let

where the are the slopes (and the ranks) in the Harder-Narasimhan filtration of , and for every prime number let

where the are the slopes in the strong Harder-Narasimhan filtration of on the fiber .

Then