English

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}
}

Comments

21 pages

R2 v1 2026-06-21T18:16:09.795Z