A finiteness property of graded sequences of ideals

2010/11/17 by Mattias Jonsson, Jonsson, Mattias, Mircea Mustata +1
Mathematics · #14B05 (Secondary) #14F18 (Primary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:14B05 #msc:14F18

paper · pdf · doi:10.48550/arxiv.1011.3967

9 pages; v2: final version, to appear in Algebra and Number Theory

arxiv created 2011/07/04 · arxiv updated 2011/07/05

Abstract

Given a graded sequence of ideals (a_m) on a smooth variety X having finite log canonical threshold, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log discrepancies of the divisors E_m are bounded. We show that in this case the set of divisors E_m is finite.

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