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algebraic curves, algebraic manifolds and schemes
Algebraicheskai︠a︡ geometrii︠a︡ 1. English
Shafarevich, I. R. (Igorʹ Rostislavovich)
1 online resource (307 pages) : illustrations
This book 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 immensely useful to mathematicians working in algebraic geometry and complex analysis and especially to graduate students in these fields.
I. Riemann Surfaces and Algebraic Curves / V.V. Shokurov -- II. Algebraic Varieties and Schemes / V.I. Danilov.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
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Includes bibliographical references (pages 294-297) and indexes.
Berlin ; New York : Springer-Verlag, c1994
Encyclopaedia of mathematical sciences ; v. 23
3540519955 (Springer-Verlag Berlin Heidelberg New York)
9783540519959 (Springer-Verlag Berlin Heidelberg New York)
0387519955 (Springer-Verlag New York Berlin Heidelberg)
9780387519951 (Springer-Verlag New York Berlin Heidelberg)