On monotonicity of F-blowup sequences

For each variety in positive characteristic, there is a series of canonically defined blowups, called F-blowups. We are interested in the question of whether the (e + 1)th blowup dominates the eth, locally or globally. It is shown that the answer is affirmative (globally for any e) when the given variety is Fpure. As a corollary, we obtain some result on the stability of the sequence of F-blowups. We also give a sufficient condition for local domination.