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arXiv · 2102.07080

Multiplicities of Jumping Numbers

Suchitra Pande
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Abstract

We study multiplicities of jumping numbers of multiplier ideals in a smooth variety of arbitrary dimension. We prove that the multiplicity function is a quasi-polynomial, hence proving that the Poincar\'e series is a rational function. We further study when the various components of the quasi-polynomial have the highest possible degree and relate it to jumping numbers contributed by Rees valuations. Finally, we study the special case of monomial ideals.

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Suchitra Pande. 2021-02-14. Multiplicities of Jumping Numbers. https://doi.org/10.2140/ant.2023.17.83

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