Introduction to the Minimal Model Program, Sommersemester 2023

Dozent: Prof. Dr. Vladimir Lazić

The course will be taught in English in presence and/or online.

Dates: Wednesdays 10-12 in SR10 or online


This is a course on recent progress in higher dimensional birational geometry in characteristic zero, and in particular in the Minimal Model Program. I will cover (most of) the following:

  • the aim of the birational classification of (higher dimensional) algebraic varieties, and obstacles in dimension at least 3,
  • pairs and their singularities,
  • birational contrations, the importance of being Q-Gorenstein,
  • finite generation of the canonical ring and the existence of flips,
  • the Cone theorem and the basepoint free theorem,
  • termination of special flips,
  • rational curves, reduction to positive characteristic and bend-and-break (if time permits).

Prerequisites: Algebraic Geometry as in Hartshorne "Algebraic Geometry" and in Lazarsfeld "Positivity in Algebraic Geometry I, II".

Exam Dates

The exam will be an oral exam, the dates will be individually arranged. 

Important: If you cannot register in the LSF for the exam, please send me an email (your Prüfungssekretariat has to send me a confirmation that you are allowed to take part in the exam in time before the exam). If your Prüfungsordnung allows it, you may use the second try to improve the grade.


The course rests on the notes here.


Fachrichtung Mathematik
Campus, Gebäude E2 4
Universität des Saarlandes
66123 Saarbrücken