Math 615 -- Vanishing Theorems, Multiplier Ideals and their Applications

Spring, 2016

Multiplier ideals are ideals of algebraic or holomorphic functions that measure in a subtle way the singularities of divisors of linear series. They arise in modern generalizations of the classical Kodaira vanishing theorem, and have found many applications in both local and global algebraic geometry. The purpose of this class is to give a survey of this curcle of ideas.

References:

1. De Fernex, Ein and Mustata, Forthcoming book on singularities and birational geometry

2. Lazarsfeld, Positivity in Algebraic Geometry

3. Lazarsfeld, A short course on multiplier ideals