Complex Algebraic Surfaces [Paperback]

A lucid and concise account of the classification of algebraic surfaces.Developed over more than a century, the classification of algebraic surfaces is still an active area of research today. This concise account, expressed simply in the language of modern topology and sheaf theory, is accessible to any graduate geometry student.Developed over more than a century, the classification of algebraic surfaces is still an active area of research today. This concise account, expressed simply in the language of modern topology and sheaf theory, is accessible to any graduate geometry student.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.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. Castelnuovos 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.& a lucid and concise account of the subject. LEnseignement Math?matique