Classification of Complex Algebraic Surfaces

Τhe classification of complex algebraic surfaces is a very classical subject which goes back to the old Italian school of algebraic geometry with Enriques and Castelnuovo. However, the exposition in the present book is modern and follows Mori's approach to the classification of algebraic varieties. The text includes the $P_{12}$ theorem, the Sarkisov programme in the surface case and the Noether–Castelnuovo theorem in its classical version.

This book serves as a relatively quick and handy introduction to the theory of algebraic surfaces and is intended for readers with a good knowledge of basic algebraic geometry. Although an acquaintance with the basic parts of books like Principles of Algebraic Geometry by Griffiths and Harris or Algebraic Geometry by Hartshorne should be sufficient, the author strove to make the text as self-contained as possible and, for this reason, a first chapter is devoted to a quick exposition of some preliminaries.