Log canonical thresholds, F-pure thresholds, and non-standard extensions
Algebraic Geometry
2011-06-02 v1 Commutative Algebra
Abstract
We present a new relation between an invariant of singularities in characteristic zero (the log canonical threshold) and an invariant of singularities defined via the Frobenius morphism in positive characteristic (the F-pure threshold). We show that the set of limit points of sequences of the form (c_p), where c_p is the F-pure threshold of an ideal on an n-dimensional smooth variety in characteristic p, coincides with the set of log canonical thresholds of ideals on n-dimensional smooth varieties in characteristic zero. We prove this by combining results of Hara and Yoshida with non-standard constructions.
Keywords
Cite
@article{arxiv.1106.0207,
title = {Log canonical thresholds, F-pure thresholds, and non-standard extensions},
author = {Bhargav Bhatt and Daniel J. Hernandez and Lance E. Miller and Mircea Mustata},
journal= {arXiv preprint arXiv:1106.0207},
year = {2011}
}
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21 pages