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The jumping coefficients of non-Q-Gorens...
Graf, Patrick...

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The jumping coefficients of non-Q-Gorenstein multiplier ideals by Graf, Patrick ( Author )
Lemonjar Open Access
N.A
19-10-2014
Let a⊂OX 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,ac) which coincides with the usual notion whenever the canonical divisor KX 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 KX 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⊂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.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1410.5091
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