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Algebraic Geometry I : Algebraic Curves, Algebraic Manifolds and Schemes - V.I. Danilov

Algebraic Geometry I

Algebraic Curves, Algebraic Manifolds and Schemes

By: V.I. Danilov, V.V. Shokurov, I. R. Shafarevich (Editor), D. Coray (Translator), V.N. Shokurov (Translator)

Hardcover

Published: 15th December 2006
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This volume of the Encyclopaedia consists of two parts. The first is devoted to the theory of curves, which are treated from both the analytic and algebraic points of view. Starting with the basic notions of the theory of Riemann surfaces the reader is lead into an exposition covering the Riemann-Roch theorem, Riemann's fundamental existence theorem, uniformization and automorphic functions. The algebraic material also treats algebraic curves over an arbitrary field and the connection between algebraic curves and Abelian varieties. The second part is an introduction to higher-dimensional algebraic geometry. The author deals with algebraic varieties, the corresponding morphisms, the theory of coherent sheaves and, finally, the theory of schemes. This book is a very readable introduction to algebraic geometry and will be very useful to mathematicians working in algebraic geometry and complex analysis and especially to graduate students in these fields.

From the reviews: "This volume... consists of two papers. The first, written by V.V. Shokurov, is devoted to the theory of Riemann surfaces and algebraic curves. It is an excellent overview of the theory of relations between Riemann surfaces and their models - complex algebraic curves in complex projective spaces. ... The second paper, written by V.I. Danilov, discusses algebraic varieties and schemes. ... I can recommend the book as a very good introduction to the basic algebraic geometry." European Mathematical Society Newsletter, 1996 "... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." Acta Scientiarum Mathematicarum

Riemann Surfaces and Algebraic Curves
Algebraic Varieties and Schemes
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540519959
ISBN-10: 3540519955
Series: Encyclopaedia of Mathematical Sciences
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 310
Published: 15th December 2006
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.9
Weight (kg): 1.39