Algebra III - Algebraic Geometry: An Introduction
Instructor Sorin Popescu (office: Math 4-119, tel. 632-8358, e-mail firstname.lastname@example.org)
A solid foundation in abstract algebra, linear algebra and field theory (such as the first year graduate courses in algebra MAT 534 and MAT 535), and perhaps some knowledge of elementary commutative algebra/algebraic geometry, topology, and complex analysis. MAT 536 is designed as an introductory course and I will try to keep the amount of required previous knowledge to a minimum.
Algebraic Geometry: A first course, by Joe Harris, GTM 133, Springer Verlag 1995.
This is an example-oriented book which gives a gentle introduction to classical algebraic geometry.
Writen in an informal style it is intended for a first course in algebraic geometry and is recommended to graduate students and
possibly some advanced undergraduates who have had extensive experience in abstract algebra.
Other recommended texts:
We will try to cover the topics in both Part I (Examples of Varieties and Maps), and Part II (Attributes of Varieties) of the textbook. The spirit of the book is to study a substantial amount of examples without developing extensive amounts of theory, while minimizing the technical algebraic prerequisities. This approach may seem somewhat unusual, but it works well for learning algebraic geometry - especially if one wants to have a good intuitive grasp of what the theorems really mean.
We may skip around a bit especially for the first few weeks:
I will assign problems in each lecture, ranging in difficulty from routine to more challenging. Course grades will be based on these problems (and any other participation); solving at least half of them will be considered a perfect score.
Concrete problems such as the study of certain explicitly given (i.e. by equations) algebraic varieties can be successfully attacked with the help of specialized computer algebra systems: