Elementary Algebraic Geometry
About this Title
Klaus Hulek, Universität Hannover, Hannover, Germany. Translated by Helena Verrill
Publication: The Student Mathematical Library
Publication Year 2003: Volume 20
ISBNs: 978-0-8218-2952-3 (print); 978-1-4704-2134-2 (online)
MathSciNet review: MR1955795
MSC: Primary 14-01
This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory.
The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
Advanced undergraduates, graduate students, and research mathematicians interested in algebra and algebraic geometry; those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.
Table of Contents
- Chapter 0. Introduction
- Chapter 1. Affine varieties
- Chapter 2. Projective varieties
- Chapter 3. Smooth points and dimension
- Chapter 4. Plane cubic curves
- Chapter 5. Cubic surfaces
- Chapter 6. Introduction to the theory of curves