On monotonicity 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 -th blowup dominates the -th, locally or globally. It is shown that the answer is affirmative (globally for any ) 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.
Keywords
Cite
@article{arxiv.0803.3373,
title = {On monotonicity of F-blowup sequences},
author = {Takehiko Yasuda},
journal= {arXiv preprint arXiv:0803.3373},
year = {2024}
}
Comments
10 pages, v.2: major revision. the title modified. the proof of the main result simplified. a key argument in v.1 is now stated as Theorem 1.3. the toric case is now explained with more details (Section 5), v.3: to appear in Illinois J. Math., arguments in the toric case improved, It is proved that the F-blowup does not preserve the F-purity