Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book contains numerous examples and exercises illustrating the theory.
Author(s): Miles Reid
Series: London Mathematical Society Student Texts
Publisher: Cambridge University Press
Year: 1989
Language: English
Pages: 140
Series: London Mathematical Society Student Texts......Page 2
Title: Undergraduate Algebraic Geometry......Page 4
Copyright......Page 5
Preface......Page 6
Contents......Page 8
§0. Woffle......Page 10
§1. Plane conics......Page 18
§2. Cubics and the group law......Page 36
Appendix to Chapter 1. Curves and their genus......Page 52
§3. Affine varieties and the Nullstellensatz......Page 57
§4. Functions on varieties......Page 75
§5. Projective and birational geometry......Page 88
§6. Tangent space and nonsingularity, dimension......Page 103
§7. The 27 lines on a cubic surface......Page 111
§8. Final comments......Page 123
Index......Page 138
