中科院数学与系统科学研究院
数学研究所
代数几何研讨班
报告人: 张鸣一 博士（美国西北大学）
题 目：Multiplier ideals of analytically irreducible plane curves
时 间：2019年08月16日 10:00-12:00
地 点：数学院南楼N602室
摘 要： I will give a crash introduction to multiplier ideals and their applications in birational
geometry. It is hard to compute multiplier ideals in general, but I will describe a formula for
multiplier ideals of analytically irreducible plane curve.
题 目：A glimpse of Hodge ideals
时 间：2019年08月16日 14:00-16:00
地 点：数学院南楼N224室
摘 要：I will define 1st Hodge ideals for reduced divisors in a way of birational geometry
and introduce some applications.
题 目：V-filtration of D-modules and Hodge filtration of Hodge modules
时 间：2019年08月17日 10:00-12:00
地 点：数学院南楼N224室
摘 要：To define Hodge ideals for Q-divisors, I will introduce the Kashiwara-Malgrange
V-filtrations of D-modules and Hodge filtrations on Hodge modules. V-filtration is also
useful in studying Bernstein-Sato polynomials.
题 目： Hodge ideals—a generalization of multiplier ideals
时 间：2019年08月18日 10:00-12:00
地 点：数学院南楼N224室
摘 要：I will introduce the definition of Hodge ideals for Q-divisors and see how Hodge
ideals generalizes multiplier ideals from a birational-geometric point of view. We will see
an example of computing Hodge ideals by Saito’s formula for Hodge filtration of Hodge
modules (and hence Hodge ideals) associated to a reduced divisor with weighted
homogeneous isolated singularities.
题 目： Hodge ideals for Q-divisors in special cases
时 间：2019年08月23日 9:00-11:00
地 点：数学院南楼N213室
摘 要： I will give formulas of Hodge filtration and Hodge ideals for Q-divisors in two
case: (1) with weighted homogeneous isolated singularities;(2) with non-degenerated Newton
boundary. I will show the connection between roots of Bernstein-Sato polynomials and
jumping numbers of Hodge ideals in the first case.
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