The classification of algebraic surfaces is an intricate and fascinating branch of mathematics, developed over more than a century and still an active area of research today. In this book, Professor Beauville gives a lucid and concise account of the subject, expressed simply in the language of modern topology and sheaf theory, and accessible to any budding geometer. A chapter on preliminary material ensures that this volume is self-contained while the exercises succeed both in giving the flavor of the classical subject, and in equipping the reader with the techniques needed for research. The book is aimed at graduate students in geometry and topology.
Table of ContentsIntroduction; 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.