Complex Algebraic Surfaces

A lucid and concise account of the classification of algebraic surfaces.

Arnaud Beauville (Author)

9780521495103, Cambridge University Press

Hardback, published 4 July 1996

144 pages, 50 exercises
23.6 x 16 x 1.5 cm, 0.363 kg

‘… a lucid and concise account of the subject.’ L’Enseignement Mathématique

Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.

Introduction
Notation
Part I. The Picard Group and the Riemann-Roch Theorem: Part II. Birational Maps: Part III. Ruled Surfaces: Part IV. Rational Surfaces: Part V. Castelnuovo’s Theorem and Applications: Part VI. Surfaces With pg = 0 and q > 1: Part VII. Kodaira Dimension: Part VIII. Surfaces With k = 0: Part IX. Surfaces With k = 1 and Elliptic Surfaces: Part X. Surfaces of General Type: Appendix A. Characteristic p
Appendix B. Complex surfaces
Appendix C. Further reading
References
Index.

Subject Areas: Applied mathematics [PBW]