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Classical Algebraic Geometry: A Modern View
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  • Title Classical Algebraic Geometry: A Modern View
  • Author(s) Igor V. Dolgachev
  • Publisher: Cambridge University Press; 1st edition (October 8, 2012)
  • Hardcover 647 pages
  • eBook PDF (722 pages, 3.1 MB)
  • Language: English
  • ISBN-10: 1107017653
  • ISBN-13: 978-3642725494
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Book Description

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times.

This detailed exposition makes the rich legacy of classical algebraic geometry accessible to modern algebraic geometers and to others who are interested in applying classical results. Topics include plane algebraic curves of low degree, special algebraic surfaces, theta functions and Cremona transformations.

About the Authors
  • Igor V. Dolgachev is Professor Emeritus in the Department of Mathematics at the University of Michigan.
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