Vol. 6, No. 7, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Log canonical thresholds, $F$-pure thresholds, and nonstandard extensions

Bhargav Bhatt, Daniel J. Hernández, Lance Edward Miller and Mircea Mustaţă

Vol. 6 (2012), No. 7, 1459–1482

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 (cp), where cp 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 nonstandard constructions.

$F$-pure threshold, log canonical threshold, ultrafilters, multiplier ideals, test ideals
Mathematical Subject Classification 2010
Primary: 13A35
Secondary: 13L05, 14B05, 14F18
Received: 1 June 2011
Revised: 16 November 2011
Accepted: 20 December 2011
Published: 4 December 2012
Bhargav Bhatt
Department of Mathematics University of Michigan
Ann Arbor, MI 48109
United States
School of Mathematics
Institute for Advanced Study
Princeton, NJ 08540
United States
Daniel J. Hernández
Department of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States
Lance Edward Miller
Department of Mathematics
University of Utah
Salt Lake City, UT 84112
United States
Mircea Mustaţă
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109
United States