Introduction to the Minimal Model Program, Wintersemester 2024/25

Dozent: Prof. Dr. Vladimir Lazić

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

Dates: Wednesdays 10-12 and 14-16, in SR6 or online

Topics

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),
• Abundance conjecture.

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