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Multiplicities of jumping numbers

Swaraj Pande

Vol. 17 (2023), No. 1, 83–110

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

multiplier ideals, jumping numbers, Poincaré series, Rees valuations, monomial ideals
Mathematical Subject Classification
Primary: 14F18
Secondary: 13D40
Received: 12 March 2021
Revised: 15 November 2021
Accepted: 4 March 2022
Published: 24 March 2023
Swaraj Pande
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States

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