Overview
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.
Full Product Details
Author: V.I. Danilov ,
I. Shafarevich ,
D. Coray ,
V.V. Shokurov
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 1st ed. 1994. 2nd printing 2006
Volume: 23
Dimensions:
Width: 15.50cm
, Height: 1.90cm
, Length: 23.50cm
Weight: 1.390kg
ISBN: 9783540519959
ISBN 10: 3540519955
Pages: 310
Publication Date: 10 March 1994
Audience:
College/higher education
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
"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"
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
