Complex Algebraic Surfaces (London Mathematical Society Student Texts)
Cambridge University Press
Edition: 2, 7/4/1996
EAN 9780521495103, ISBN10: 0521495105
Hardcover, 144 pages, 23.6 x 16 x 1.5 cm
Language: English
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.