Real Algebraic Surfaces

TL;DR

This paper provides an introduction to real algebraic surfaces, focusing on their classification and the application of the minimal model program, with historical context and comprehensive results on rational and Del Pezzo surfaces.

Contribution

It offers a systematic overview of real algebraic surfaces using the minimal model program, including a complete classification of real rational and Del Pezzo surfaces.

Findings

Complete topological classification of real Del Pezzo surfaces

Understanding of real rational surfaces through minimal model program

Historical insights from Comessatti and Silhol's works

Abstract

These are the notes for my lectures at the Trento summer school held September 1997. The aim of the lectures is to provide an introduction to real algebraic surfaces using the minimal model program. This leads to a fairly complete understanding of real rational surfaces and to a complete topological classification of real Del Pezzo surfaces. Almost all the results are contained in the works of Comessatti and Silhol.