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).
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. |