Vol. 6, No. 7, 2012

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

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

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
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
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
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 (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.

Keywords
$F$-pure threshold, log canonical threshold, ultrafilters, multiplier ideals, test ideals
Mathematical Subject Classification 2010
Primary: 13A35
Secondary: 13L05, 14B05, 14F18
Milestones
Received: 1 June 2011
Revised: 16 November 2011
Accepted: 20 December 2011
Published: 4 December 2012
Authors
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