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：戚鲁（普林斯顿大学）

题  目：Filtrations, multiplicities and singularities

时  间：2024.04.18（星期四），10:00-11:00

地  点：南楼 818

摘  要：Graded sequences of ideals, or filtrations on local rings, play an important role in commutative algebra, the theory of singularities and birational geometry. In this talk, I will introduce the saturation of a filtration and discuss several results about multiplicities of filtrations. The first is a theorem generalizing Rees' theorem on Hilbert-Samuel multiplicities of ideals. Then I will talk about convexity of multiplicities along geodesics, with applications in valuation theory and K-stability. I will also introduce a metric on the space of filtrations as an analogue of the Darvas metric in complex geometry, and prove the semiconuity of log canonical threshold functions in the spirit of Kollár-Demailly. This talk is partially based on joint work with Harold Blum and Yuchen Liu.