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 Poincaré series for mixed multiplier ideals and prove its rationality. Finally, we study the set of divisors that contribute to the log-canonical wall.

中文翻译：

---

混合乘数理想的跳跃点的多重性

在本文中，我们对具有奇异点的复杂曲面中与一族理想的混合乘数理想相关的跳跃点的复数进行了系统研究。特别地，我们通过跳跃点的小扰动来研究多重性的行为。我们还介绍了用于混合乘数理想的Poincaré系列，并证明了其合理性。最后，我们研究了构成对数正则壁的除数集。