Multiplicities of Jumping Numbers
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Publication:6360548
DOI10.2140/ANT.2023.17.83zbMath1518.14031arXiv2102.07080MaRDI QIDQ6360548
Publication date: 14 February 2021
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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