Elementary Algebraic Geometry

Forside
American Mathematical Soc., 2003 - 213 sider
This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra. 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. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.
 

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Innhold

Chapter 0 Introduction
1
Chapter 1 Affine Varieties
17
Chapter 2 Projective Varieties
63
Chapter 3 Smooth Points and Dimension
97
Chapter 4 Plane Cubic Curves
115
Chapter 5 Cubic Surfaces
143
Chapter 6 Introduction to the Theory of Curves
167
Bibliography
207
Index
211
Back Cover
216
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