Multiplicities of jumping numbers Article Swipe
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Swaraj Pande
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.2140/ant.2023.17.83
· OA: W3131825805
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.2140/ant.2023.17.83
· OA: W3131825805
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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