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Complex Algebraic Curves (London Mathematical Society Student Texts) Paperback – February 20, 1992

ISBN-13: 978-0521423533 ISBN-10: 0521423538

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Complex Algebraic Curves (London Mathematical Society Student Texts) + Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5) + Algebraic Geometry (Graduate Texts in Mathematics)
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Product Details

  • Series: London Mathematical Society Student Texts (Book 23)
  • Paperback: 276 pages
  • Publisher: Cambridge University Press (February 20, 1992)
  • Language: English
  • ISBN-10: 0521423538
  • ISBN-13: 978-0521423533
  • Product Dimensions: 6 x 0.6 x 9 inches
  • Shipping Weight: 15.5 ounces (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,085,624 in Books (See Top 100 in Books)

Editorial Reviews

Review

"Kirwan should succeed admirably with her goal of showing senior undergraduates who perhaps do not plan to study mathematics beyond the bachelor's degree 'how the basic ideas of pure mathematics they had studied in previous years could be brought together in one of the showpieces of mathematics.'" Choice

"...worth serious consideration for those planning to teach such a course, and perhaps even more importantly, as an inspiration for mathematicians to offer such a course. The book offers us plenty to work with, and is an excellent contribution." S. Zdravkovska and Daniel M. Burns, Jr., Mathematical Reviews

"At last an introduction to the theory of algebraic curves that is understandable by undergraduates, and that does not shy away from the various aspects of the theory: algebraic, topological, complex analytic, etc. Good bedside reading." Gian-Carlo Rota, The Bulletin of Mathematical Books

Book Description

Using only basic undergraduate mathematical techniques, the author introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

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9 of 10 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on March 14, 2001
Format: Paperback
The book gives a good general overview of algebraic curves using only elementary algebra, topology, and complex analysis. There are lots of diagrams of elliptic curves in the historical introduction in the first chapter and the subject is well motivated. Hilbert's Nullstellensatz is introduced in the context of real algebraic curves as an answer to the question of when the polynomials definte the same curve. The visualization approach taken by the author in the first chapter has taken on dramatic proportions do to the computer graphics packages currently available. The author introduces complex algebraic curves in complex 2-dimensional space in the next chapter. Recognizing that such curves are not compact, he compactifies them by adding suitable points at infinity, giving complex projective curves. The algebraic properties of these curves are studied in the next chapter. He does a good job of motivating the group law on elliptic curves on the last theorem of the chapter, leaving the proof of associativity to the reader in the exercises. The topology of complex projective curves is taken up in Chapter 4. The author gives two proofs of the degree-genus formula, one geometric and the other from a holomorphic point of view. This leads to a consideration of branch points and ramified covers. The author's outline of the proofs is very detailed and therefore very helpful to one encountering the proof for the first time. The statement of the formula via the Riemann-Roch theorem in more formal treatments (and later in the book) can then be appreciated more. The subject of non-singular complex projective curves, namely Riemann surfaces, is effectively discussed in Chapter 5, with holomorphic differentials outlined in Chapter 6.Read more ›
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0 of 3 people found the following review helpful By Daz on June 17, 2014
Format: Paperback Verified Purchase
I've been ordering books from Amazon -- both new and used -- since 1997. This book was advertised as in "like new" condition.

This is the only time ever that I received a book so fragile that the first time I tried to read it -- gently! -- the spine broke. As I tried to view various pages, the spine broke in a new place each time.

I would not recommend using this vendor.
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4 of 19 people found the following review helpful By A Customer on May 13, 2003
Format: Paperback
This is a very nice, short introduction to the subject -- This series of blue paperbacks by CUP is excellent. Typically, all books in the series are readable introductions. Somewhat higher level than the corresponding series from Springer (the one where all exercises have full solutions).
Incidentally, the author is a very attractive woman.
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