Arbeitsgruppe Lazić

Algebraic and Complex Geometry


Prof. Dr. Vladimir Lazić

Introduction to the Minimal Model Program, Sommersemester 2017

Mi, Do 14-16 in SR 10, Gebäude E2 4

The course rests on the notes here. The intended audience are motivated Master students and above.

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).
The course prerequisites rest on this course I gave in the Wintersemester 2013/14, but I might include different topics depending on the audience.

Further reading

[1] R. Lazarsfeld, Positivity in Algebraic Geometry. II, Springer-Verlag, Berlin, 2004.
[2] S. Iitaka, Algebraic Geometry, Springer-Verlag, New York, 1982.
[3] O. Debarre, Higher-Dimensional Algebraic Geometry, Springer-Verlag, New York, 2001.
[4] J. Kollár, S. Mori, Birational Geometry of Algebraic Varieties, Cambridge University Press, Cambridge, 1998.