Friday, April 19, 2013

An Invitation to Algebraic Geometry by Karen E. Smith

An Invitation to Algebraic Geometry PDF Download Ebook. Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen and William Traves describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today.

It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra. The author has some stunning graphs and pictures to help understand material. Long stretches of the book apply just as well over any field or any algebraically complete field.

This book sets aside a lot of the tedious background required to get started in algebraic geometry and lets you get acquainted with the actual ideas of the subject. The book does geometry over the complex numbers. It is good old conservative material, with terrific graphics of curves and surfaces. The proofs and partial proofs are very clear, intuitive and to the point.

Affine Algebraic Varieties.- Algebraic Foundations.- Projective Varieties.- Quasi-projective Varieties.- Classical Constructions.- Smoothness.- Birational Geometry.- Maps to Projective Space.- Appendix: Sheaves and Abstract Varieties.

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