Complex Algebraic Surfaces - Spring 2018

Time and Place : MW 10-11:20; Math 4-130

Instructor : Radu Laza

Office : Math Tower 4-121
Email :  radu.laza@stonybrook.edu

Office Hours: Wed 1-3pm

Overview

References:

• [B] A. Beauville, Complex Algebraic Surfaces -- this is the main reference that we will use during the semester.
• [F] R. Friedman, Algebraic Surfaces and Holomorphic Vector Bundles -- a complementary reference (for some topics we will use this).
• [B et al.] W. Barth, K. Hulek, C. Peters, A.van de Ven - Compact Complex Surfaces - a more analytic point of view.
• [KM] J. Kollár, S. Mori - Birational Geometry of Algebraic Varieties - the standard reference for birational geometry/MMP (this will come handy occasionally, and it is a natural follow-up text)
• [H] D. Huybrechts - Lectures on K3 Surfaces - more details on the very important topic of K3 surfaces.

Topics Discussed: The purpose of the course is to discuss the Castelnuovo-Enriques classification of surfaces. We will follow mostly Beauville's book, but with a greater emphasis on the MMP point of view (i.e. more focus on the behavior of the canonical class). We will spend some extra time on some special classes of surfaces, such as del Pezzo and K3 surfaces. With an eye on the higher dimensional case, I will introduce various classes of singularities and I will explain how they naturally occur.

Schedule