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Elementary Algebraic Geometry
Klaus Hulek, Universität Hannover, Germany
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Student Mathematical Library
2003; 213 pp; softcover
Volume: 20
ISBN-10: 0-8218-2952-1
ISBN-13: 978-0-8218-2952-3
List Price: US$39
Institutional Members: US$31.20
All Individuals: US$31.20
Order Code: STML/20
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See also:

Plane Algebraic Curves - Gerd Fischer

This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra.

The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory.

The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

Readership

Advanced undergraduates, graduate students, and research mathematicians interested in algebra and algebraic geometry; those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

Reviews

"The book balances theory and examples well and the exercises are well-chosen to further illustrate the basic concepts. All in all, the book does an excellent job of explaining what algebraic geometry is about, what are the basic results, and it invites the reader to continue exploring the subject ... I would definitely recommend it as reading material to a bright undergraduate who has taken a basic course on rings and fields and has read about Noetherian rings. It is certainly suitable for a one-semester graduate course ... Mathematicians from other areas will also enjoy the book ... [It] reminds me of more old-fashioned books on algebraic geometry ... but updated to our modern standards of rigor and shorter attention span."

-- MAA Online

From a review for the German Edition:

"The introduction contains numerous examples which illustrate and motivate the discussed theory and which reappear, as the course develops, handled in a precise and clear manner ... Each section ends with interesting and doable (!) exercises ... the author makes a great effort to prove most of the theorems in the rigorous way ... Precision and clarity are distinguished features of the reviewed test."

-- MathSciNet, Mathematical Reviews on the Web

"The book remains one of the very best introductory texts on algebraic geometry. The last chapter is a masterpiece of didactic art ... absolutely unique for such an elementary textbook."

-- Zentralblatt MATH

Table of Contents

  • Introduction
  • Affine varieties
  • Projective varieties
  • Smooth points and dimension
  • Plane cubic curves
  • Cubic surfaces
  • Introduction to the theory of curves
  • Bibliography
  • Index
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