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.
Readership
Graduate students and researchers interested in algebraic
geometry.
