- Series: Student Mathematical Library, V. 20 (Book 20)
- Paperback: 213 pages
- Publisher: American Mathematical Society (February 13, 2003)
- Language: English
- ISBN-10: 0821829521
- ISBN-13: 978-0821829523
- Product Dimensions: 0.5 x 5.8 x 8.5 inches
- Shipping Weight: 8 ounces (View shipping rates and policies)
- Average Customer Review: 3 customer reviews
- Amazon Best Sellers Rank: #1,204,144 in Books (See Top 100 in Books)
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Elementary Algebraic Geometry (Student Mathematical Library, Vol. 20) (Student Mathematical Library, V. 20)
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"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 ---- Zentralblatt MATH
Text: English (translation)
Original Language: German
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As so often happens, this book looked great in the bookstore. It is thin, reasonably well-illustrated compared to other books in the field, and even helps you gets your toes wet in sheaves, category theory and some other neat topics.
That said, I believe the prerequisites in the preface (university algebra, with a complex variables course optional) are understated; e.g. it helps to know something about fibres, lifts and other topics from geometry. It might be relevant that these notes were prepared at a German university; you should consider that "undergraduates" there are heading toward the equivalent of a US M.S. degree, not B.S./B.A.
More detrimental is that the presentation slogs from one proof to another and too rarely pauses for breath to consider the "big picture" significance of what you're proving. Notwithstanding that Joe Harris's "Algebraic Geometry: A First Course" is even less of a piece of cake for me than it might be for you, his style is a breath of fresh air when it comes to enlightening you as to some geometric context and payoff for all this effort. Other supplements I found helpful include Reid and Schenck.
PS in 2008: I very belatedly found the terrific "An Invitation to Algebraic Geometry," by Karen E. Smith &al. (Springer 2000, corrected printing 2004). This is the hands-down best introduction to the subject, IMHO.