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An Introduction to Algebraic Geometry
Kenji Ueno, Kyoto University, Japan

Translations of Mathematical Monographs
1997; 246 pp; softcover
Volume: 166
ISBN-10: 0-8218-1144-4
ISBN-13: 978-0-8218-1144-3
List Price: US$88
Member Price: US$70.40
Order Code: MMONO/166.S
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This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.


Graduate students, research mathematicians, and mathematics educators interested in algebraic geometry.


"Written by one of the most outstanding experts in contemporary algebraic geometry and its now ubiquitous applications in mathematical physics ... without any doubt, this textbook, designed for very beginners in algebraic geometry, serves its purpose in a commendable manner. It is perfectly suited for teaching (and learning) the basic ideas of algebraic geometry at the undergraduate level, written with didactic empathy and experience, and it provides sufficient background material, intuitive understanding and computational skills for a profound study of more advanced textbooks."

-- Zentralblatt MATH

"The book offers an invitation to algebraic geometry to anybody interested in understanding basic ideas and tools used in algebraic geometry ... recommend it to everybody as a nice textbook for the beginners."

-- European Mathematical Society Newsletter

Table of Contents

  • Invitation to algebraic geometry
  • Projective space and projective varieties
  • Algebraic curves
  • The analytic theory of algebraic curves
  • Commutative rings and fields (Appendix)
  • References
  • Index
  • Index for definitions, theorems, etc.
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