Cornell Math - MATH 767, Spring 2006

MATH 767: Algebraic Geometry (Spring 2006)

Instructor: Damiano Testa

Meeting Time & Room

The course will be an introduction to the classification of algebraic surfaces. For complex surfaces this was obtained by Enriques and Castelnuovo. Later developments allowed the classification of complex analytic surfaces and of algebraic surfaces in positive characteristic. These results are mainly due to Kodaira, Zariski, Mumford and Bombieri.

More recently, Mori's new ideas in the birational classification of algebraic varieties provided a different look at the theory for surfaces. His strategy gives a coarser classification, pleasantly intertwined with the classical theory.

I will present Mori's point of view and proceed to analyze how it fits in the more detailed classical theory. Plenty of beautiful examples will guide us in the analysis.

The level of the class will depend on the audience, though some familiarity with elementary algebraic geometric concepts will be assumed.