Algebraic Geometry 3: Further Study of Schemes
About this Title
Kenji Ueno, Kyoto University, Kyoto, Japan. Translated by Goro Kato
Publication: Translations of Mathematical Monographs
Publication Year: 2003; Volume 218
ISBNs: 978-0-8218-1358-4 (print); 978-1-4704-4076-3 (online)
MathSciNet review: MR1989998
MSC: Primary 14-01; Secondary 14A15, 14Hxx
This is the third part of the textbook on algebraic geometry by Kenji Ueno (the first two parts were published by the AMS as Volumes 185 and 197 of this series). Here the author presents the theory of schemes and sheaves beyond introductory notions, with the goal of studying properties of schemes and coherent sheaves necessary for full development of modern algebraic geometry.
The main topics discussed in the book include dimension theory, flat and proper morphisms, regular schemes, smooth morphisms, completion and Zariski's main theorem. The author also presents the theory of algebraic curves and their Jacobians and the relation between algebraic and analytic geometry, including Kodaira's Vanishing Theorem.
The book contains numerous exercises and problems with solutions, which makes it (together with two previous parts) appropriate for a graduate course on algebraic geometry or for self-study.
Graduate students and researchers interested in algebraic geometry.
Table of Contents
- Fundamental properties of scheme theory
- Algebraic curves and Jacobian varieties
- Algebraic geometry and analytic geometry
- Overview and references
- Solutions to problems
- Solutions to exercises