A short course on multiplier ideals

TL;DR

This paper provides an accessible introduction to multiplier ideals, emphasizing their global aspects, concrete examples, and recent developments like adjoint ideals, aimed at helping readers understand their applications in algebraic geometry.

Contribution

It offers a comprehensive, example-driven overview of multiplier ideals focusing on global properties and recent advancements, suitable for learners and researchers.

Findings

Simplifications in Siu's theorem on plurigenera

Introduction of adjoint ideals and their applications

Enhanced understanding of multiplier ideals in algebraic geometry

Abstract

These notes are the write-up of my 2008 PCMI lectures on multiplier ideals. They aim to give an introduction to the algebro-geometric side of the theory, with an emphasis on its global aspects. The focus is on concrete examples and applications. The lectures take into account a number of recent perspectives, including adjoint ideals and the resulting simplifications in Siu's theorem on plurigenera in the general type case. While the notes refer to my book [PAG] and other sources for some technical points, the conscientious reader should arrive at a reasonable grasp of the machinery after working through these lectures.