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Algebraic Geometry (Dover Books On Mathematics)

This text for advanced undergraduate students is both an introduction to algebraic geometry and a bridge between its two parts — the analytical-topological and the algebraic. Because of its extensive use of formal power series (power series without convergency), the treatment will appeal to readers conversant with analysis but less familiar with the formidable techniques of modern algebra.The book...

Series: Dover Books on Mathematics
Paperback: 256 pages
Publisher: Dover Publications (December 27, 2005)
Language: English
ISBN-10: 0486446115
ISBN-13: 978-0486446110
Product Dimensions: 5.5 x 0.5 x 8.5 inches
Amazon Rank: 1142494
Format: PDF Text TXT book

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“I am glad that this original from PUP is reprinted. It covers a bit more than the van der Waerden's "Einfuerung in die algebraische geometrie" in the same old style. A readable equivalent in modern language is the Shafarevich's "basic AG". These book...”

opens with an overview of the results required from algebra and proceeds to the fundamental concepts of the general theory of algebraic varieties: general point, dimension, function field, rational transformations, and correspondences. A concentrated chapter on formal power series with applications to algebraic varieties follows. An extensive survey of algebraic curves includes places, linear series, abelian differentials, and algebraic correspondences. The text concludes with an examination of systems of curves on a surface.