Algebraic and Analytic Geometry

Amnon Neeman is professor of mathematics at Australian National University. He is the author of the book Triangulated Categories.

• Foreword; 1. Introduction; 2. Manifolds; 3. Schemes; 4. The complex topology; 5. The analytification of a scheme; 6. The high road to analytification; 7. Coherent sheaves; 8. Projective space - the statements; 9. Projective space - the proofs; 10. The proof of GAGA; Appendix. The proofs concerning analytification; Bibliography; Glossary; Index.

'All in all, the book under review is a masterpiece of expository writing in modern algebraic geometry. It is exactly what the author promised: no comprehensive text to train future algebraic geometers, but rather an attempt to convince students of the fascinating beauty, the tremendous power, and the high value of the methods of algebraic and analytic geometry. The author has reached his declared goal in an admirable, truly brilliant manner. His lucid exposition of these modern, fairly advanced topics in the field for beginners breathes his passion for the subject and for grippingly teaching it, and his style of writing bespeaks a good sympathetic understanding of students and their needs.' Werner Kleinert, Zentralblatt MATH