Multiplicities of Jumping Numbers
arXiv:2102.07080 · doi:10.2140/ant.2023.17.83
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 Poincaré 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.
24 pages, Final version, Appeared in Algebra & Number Theory. Minor changes in v3 :)