A finiteness property of graded sequences of ideals

Jonsson, Mattias; Mustaţă, Mircea

doi:10.2140/ant.2012.6.561

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A finiteness property of graded sequences of ideals

Mattias Jonsson and Mircea Mustaţă

Vol. 6 (2012), No. 3, 561–571

DOI: 10.2140/ant.2012.6.561

Abstract

Given a graded sequence of ideals ${(a_{m})}_{m \geq 1}$ on $X$ , having finite log canonical threshold, we show that if there are divisors $E_{m}$ over $X$ computing the log canonical threshold of $a_{m}$ , and such that the log discrepancies of the divisors $E_{m}$ are bounded, then the set ${E_{m} ∣ m \geq 1}$ is finite.

Keywords

graded sequence of ideals, log canonical threshold

Mathematical Subject Classification 2010

Primary: 14F18

Secondary: 14B05

Milestones

Received: 27 November 2010

Revised: 23 May 2011

Accepted: 30 June 2011

Published: 5 July 2012

Authors

Mattias Jonsson
Department of Mathematics University of Michigan Ann Arbor, MI 48109-1043 United States

Mircea Mustaţă
Department of Mathematics University of Michigan Ann Arbor, MI 48109-1043 United States

Vol. 6, No. 3, 2012