F-purity of hypersurfaces
Commutative Algebra
2012-02-13 v2
Abstract
In this note, we study F-purity of pairs, and show (as is the case with log canonicity) that F-purity is preserved at the F-pure threshold. We also characterize when F-purity is equivalent to sharp F-purity, an alternate notion of purity for pairs introduced in [Sch08]. These results on purity at the threshold generalize results appearing in [Har06, Sch08], and were expected to hold by many experts in the field. We conclude by extending results in [BMS09] on the set of all F-pure thresholds to the most general setting.
Cite
@article{arxiv.1112.2424,
title = {F-purity of hypersurfaces},
author = {Daniel J. Hernández},
journal= {arXiv preprint arXiv:1112.2424},
year = {2012}
}
Comments
Version 1: 12 pages, 1 figure. Comments welcome! Version 2: Minor revisions (as suggested by the referee) and updated references. To appear in Mathematical Research Letters