Algebraic Surfaces in Positive Characteristic

Details Algebraic Surfaces in Positive Characteristic Algebraic Surfaces in Positive Characteristic

2009-12-21

arxiv.org/abs/0912.4291v2

Mathematics

Algebraic Geometry

55 pages, expanded lecture notes, partly rewritten, typos corrected and many new references - comments and references welcome!

Scientific paper

These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in characteristic-$p$-geometry, we sketch the Kodaira--Enriques classification. Next, we turn to more special characteristic-$p$ topics, and end by lifting results and applications to characteristic zero. We assume that the reader has a background in complex geometry and has seen the Kodaira--Enriques classification of complex surfaces before.

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