Methods of Algebraic Geometry in Char, P and Their Applications

Abstract

I. The aim of these lectures is to illustrate some of the algebraic techniques needed for algebraic geometry in char, p, with a particular view to the theory of algebraic surfaces and Enriques' classification. We shall study the new char, p features of Kodaira's vanishing theorem, the completeness of the characteristic system and the theory of the Picard variety, together with the study of elliptic and quasi-elliptic fibrations, the study of Enriques' surfaces in char. 2 and the characterization of abelian surfaces by means of their numerical invariants.