Multiplicities of Jumping Numbers
Algebraic Geometry
2025-03-04 v3 Commutative Algebra
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.
Cite
@article{arxiv.2102.07080,
title = {Multiplicities of Jumping Numbers},
author = {Suchitra Pande},
journal= {arXiv preprint arXiv:2102.07080},
year = {2025}
}
Comments
24 pages, Final version, Appeared in Algebra & Number Theory. Minor changes in v3 :)