Theory of Algebraic Surfaces

This is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus. It also discusses the behavior of the pluri-canonical maps of surfaces of general type as a practical application of the general theory. The book is aimed at graduate students and also at anyone interested in algebraic surfaces, and readers are expected to have only a basic knowledge of complex manifolds as a prerequisite.

Discusses the fundamental topics in the theory of complex algebraic surfaces Serves as an introductory textbook for graduate students of algebraic geometry Requires only a basic knowledge of complex manifolds as a prerequisite

Résumé
"The book has an obvious historical interest ... . the exposition of many topics is extremely informative both in terms of content and style. Moreover, reading this work is highly recommended for young lovers of classical algebraic geometry and for those who want to become familiar with the theory of algebraic surfaces. Lastly, a feature of the text that makes the reading very pleasant and stimulating is the concreteness of the analytic approach that can be found at every step." (Antonio Lanteri, Mathematical Reviews, March 2022)

"The readers are expected to have only elementary prerequisites on complex manifolds and as such this book ... can be very useful for a graduate student or a non-expert starting to work on algebraic geometry." (Margarida Mendes Lopes, zbMATH 1462.14001, 2021)

Contenu
Foreword.- Preface.- Introduction (Purposes and Known Results).- Chapter: 1 Fundamentals of Algebraic Surfaces.- Chapter 2: Pluri-canonical Systems on Algebraic Surfaces of General.- Bibliography.