Undergraduate Algebraic Geometry (London Mathematical Society Student Texts, Series Number 12)

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. Algebraic Geometry Is, Essentially, The Study Of The Solution Of Equations And Occupies A Central Position In Pure Mathematics. This Short And Readable Introduction To Algebraic Geometry Will Be Ideal For All Undergraduate Mathematicians Coming To The Subject For The First Time. 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 Non-singularity And Dimension. He Is At Pains To Stress The Connections The Subject Has With Commutative Algebra As Well As Its Relation To Topology, Differential Geometry, And Number Theory. The Book Arises From An Undergraduate Course Given At The University Of Warwick And Contains Numerous Examples And Exercises Illustrating The Theory. Miles Reid. Includes Index. 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 An introduction to algebraic geometry which covers the basic concepts of plane conics, cubics and group law, affine and projective varieties, and non-singularity and dimension, the connections with commutative algebra as well as its relation to topology, differential geometry and number theory