Multiplicities of jumping points for mixed multiplier ideals

TL;DR

This paper systematically studies the multiplicities of jumping points for mixed multiplier ideals on complex surfaces with rational singularities, introduces a Poincaré series, and analyzes divisors contributing to the log-canonical wall.

Contribution

It provides a detailed analysis of jumping point multiplicities, introduces a rational Poincaré series for mixed multiplier ideals, and explores divisors affecting the log-canonical wall.

Findings

Multiplicity behavior under small perturbations analyzed

Rationality of the Poincaré series established

Characterization of divisors contributing to the log-canonical wall

Abstract

In this paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the multiplicity by small perturbations of the jumping points. We also introduce a Poincar\'e series for mixed multiplier ideals and prove its rationality. Finally, we study the set of divisors that contribute to the log-canonical wall.