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