F-thresholds of hypersurfaces
Algebraic Geometry
2011-02-18 v3 Commutative Algebra
Abstract
We continue our study of F-thresholds begun in math/0607660 by an in depth analysis of the hypersurface case. We use the D--module theoretic description of generalized test ideals which allows us to show that in any F--finite regular ring the F-thresholds of hypersurfaces are discrete and rational (in math/0607660 the finite type over a field case was shown for arbitrary ideals). Furthermore we show that any limit of F-pure thresholds of principal ideals in bouneded dimension is again an F-pure-threshold, hence in particular the limit is rational. The study of the set of F-pure-thresholds leads to natural analogs of conjectures of Shokurov and Koll\'{a}r (for log canonical thresholds) in the case of F-pure-thresholds.
Cite
@article{arxiv.0705.1210,
title = {F-thresholds of hypersurfaces},
author = {Manuel Blickle and Mircea Mustaţǎ and Karen Smith},
journal= {arXiv preprint arXiv:0705.1210},
year = {2011}
}