On monotonicity of F-blowup sequences

TL;DR

This paper investigates the monotonicity of F-blowup sequences in positive characteristic varieties, proving global domination for F-pure cases and providing conditions for local domination, thus contributing to understanding their stability.

Contribution

It establishes the global monotonicity of F-blowup sequences for F-pure varieties and offers a new sufficient condition for local domination.

Findings

F-blowup sequences are globally dominating for F-pure varieties.

A sufficient condition for local domination of F-blowups is provided.

The results imply stability properties of F-blowup sequences.

Abstract

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 $e$-th, locally or globally. It is shown that the answer is affirmative (globally for any $e$) when the given variety is F-pure. 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.