F-purity of hypersurfaces

Details F-purity of hypersurfaces F-purity of hypersurfaces

2011-12-12

arxiv.org/abs/1112.2424v2

Mathematics

Commutative Algebra

Version 1: 12 pages, 1 figure. Comments welcome! Version 2: Minor revisions (as suggested by the referee) and updated referenc

Scientific paper

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.

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