Undergraduate Algebraic Geometry

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Cambridge University Press, Dec 15, 1988 - Mathematics - 129 pages
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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.
 

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Contents

Playing with plane curves
9
2 Cubics and the group law
27
Curves and their genus
43
The category of affine varieties
48
4 Functions on varieties
66
Applications
79
6 Tangent space and nonsingularity dimension
94
7 The 27 lines on a cubic surface
102
8 Final comments
114
Index
129
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