Multiplier ideals and Siu's theorem

Reading group, Summer Semester 2015

Meet Tuesdays at 11:00 in the seminar room 1.411 on our floor (Haus 1 floor 4 room 11). Starting week 2 on the 21th of April.


Here are the final handwritten notes for the course.

Last updated: 23/6/2015


We'll mostly follow part III of Lazarsfeld's second book. The goal is to have a few introductory talks and then to get to applications:

  • Singularities of theta divisors

  • Matsusaka's big theorem

  • (optional) Nakamaye's theorem

  • (optional) Angehrn-Siu

  • Asymptotic multiplier ideals

  • (optional) Fujita approximation

  • (optional) BDPP Movable-pseff duality

  • Siu's invariance of plurigenera

Here's the outline for the talks


Talk 1/2 (Frank, 21, 28 April): Kawamata-Viehweg. This sets the mood in terms of the various cones of divisors, SNC divisors, log resolutions etc. First prove Kodaira vanishing using covering tricks, and then elaborate on KV for Q/R-divisors.

Talk 2/3 (Angela 28 April, 5 May): Definitions of multiplier ideals following Lazarsfeld 9.2, 9.3.A, 9.3.B, 9.3.E-G (we can skip monomial ideals and possibly the analytic side)

Talk 4 (Michael, 12 May): Section 9.4 - Nadel vanishing and the non-vanishing theorem

Talk 5 (Frank 19 May): Section 9.5 - Restriction, subadditivity, summation

Talk 6 (Ben 26 May): Section 10.2/10.4 - Angehrn-Siu and Matsusaka's big theorem

Talk 7 (Gregor 9 June): Section 10.1 - Singularities of hypersurfaces and theta divisors. The notes he typed up are.

Talk 8 (Niels 16 June): Asymptotic multiplier ideals, Kollar's etale multiplicativity of higher plurigenera

Talk 9 (Frank 25 June): Siu's theorem on plurigenera I

Talk 10 (Frank 30 June): Siu's theorem on plurigenera II: the extension theorem


Various references:


de Fernex-Ein-Mustata's new book

Hacon's excellent course notes on the MMP

Lazarsfeld's 2009 notes

Ein-Mustata ICM 2006 on singularities and multiplier ideals

Demailly's analytic multiplier ideals notes