The jumping coefficients of non-Q-Gorenstein multiplier ideals

JOURNAL OF ALGEBRA

卷:450

Article

Graf, Patrick¹ 

[1] Univ Bayreuth, Lehrstuhl Math 1, POB 101251, D-95440 Bayreuth, Germany

关键词: Singularities of pairs;    Multiplier ideals;    Jumping numbers;    Test ideals;   

DOI  :  10.1016/j.jalgebra.2015.11.024

来源: Elsevier

【 摘 要 】

Let a subset of (sic)(X) be a coherent ideal sheaf on a normal complex variety X, and let c >= 0 be a real number. De Fernex and Hacon associated a multiplier ideal sheaf to the pair (X, a(c)) which coincides with the usual notion whenever the canonical divisor K-X is Q-Cartier. We investigate the properties of the jumping numbers associated to these multiplier ideals. We show that the set of jumping numbers of a pair is unbounded, countable and satisfies a certain periodicity property. We then prove that the jumping numbers form a discrete set of real numbers if the locus where K-X fails to be Q-Cartier is zero-dimensional. It follows that discreteness holds whenever X is a threefold with rational singularities. Furthermore, we show that the jumping numbers are rational and discrete if one removes from X a closed subset W subset of X of codimension at least three, which does not depend on a. We also obtain that outside of W, the multiplier ideal reduces to the test ideal modulo sufficiently large primes p >> 0. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free