Classification of Algebraic Surfaces and of Stable Bundles

Abstract

In this chapter, we outline the major results in the classification theory of surfaces, and then proceed to fill in the details of the proofs. While the proofs given here do not rely on Mori theory, we give a brief description of the corresponding results for threefolds, whose proofs rely heavily on Mori theory. In the last section, we survey some of the known results on the structure of the moduli space of stable bundles over a surface, and try to relate these results to the geometry of the original surface.