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The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians (Lecture Notes in Mathematics) 2nd exp. ed. 1999 Edition

4.8 out of 5 stars 5 customer reviews
ISBN-13: 978-3540632931
ISBN-10: 354063293X
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  • The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians (Lecture Notes in Mathematics)
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  • Algebraic Geometry (Graduate Texts in Mathematics)
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Editorial Reviews

Review

"This is the second edition of a famous and well-known introduction to algebraic geometry, written to show that the language of schemes is fundamentally geometrical and clearly expressing the intuition of algebraic geometry. ... This book can strongly be recommended to anybody interested in algebraic geometry and willing to learn about varieties and schemes and their main problems."
EMS Newsletter, Vol. 37, Sept. 2000
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Product Details

  • Series: Lecture Notes in Mathematics (Book 1358)
  • Paperback: 304 pages
  • Publisher: Springer; 2nd exp. ed. 1999 edition (February 22, 2009)
  • Language: English
  • ISBN-10: 354063293X
  • ISBN-13: 978-3540632931
  • Product Dimensions: 6.1 x 0.7 x 9.2 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #951,761 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Paperback
In a nutshell, reading this book is like reading the mind of a great mathematician as he thinks about a great new idea. Anyone interested in schemes should read it. But a review needs more detail:
The RED BOOK is a concise, brilliant survey of schemes, by one of the first mathematicians to learn of them from Grothendieck. He gives wonderfully intuitive pictures of schemes, especially of "arithmetic schemes" where number theory appears as geometry. The geometry shines through it all: as in differentials, and etale maps, and how unique factorization relates to non-singularity. There is a bravura discussion of Zariski's Main Theorem (the algebraic property of being "normal" implies that a variety has only one branch at each point) comparing forms of it from older algebraic geometry, topology, power series, and schemes. Mumford cites proofs of these but does not give them. In fact, this theorem was one of the first things Mumford could use, to get Zariski to respect schemes.
Many accomplished algebraic geometers say this book got them started. But you probably cannot learn to work in the subject from this book alone--you either have to work with people who work with it, or use some other books besides (maybe both). The other book would probably be Hartshorne ALGEBRAIC GEOMETRY, which is far more detailed, has far more examples, goes very much farther into cohomology--and is very much longer and denser (though also clearly written).
Eisenbud and Harris GEOMETRY OF SCHEMES covers a lot of the same ground as THE RED BOOK, with fewer advanced topics but many more details and examples, including classical geometric constructions like blow-ups and duals to projective plane curves. They use slightly more category theory than Mumford, more like Grothendieck.
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Format: Paperback
There is a problem in getting going with alg. geo. To learn the geometry you need commutative algebra and to contextualize commutative algebra you need algebraic geometry. Mumford is an excellent book to get going without the need for the heavy prereqs of the more classic books like Hartshore or G&H. A really good read.
This is not however a terrific reference text, you'll need something else as a reference. Its much to expository and their is no index.
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Format: Paperback
Algebraic geometry is a broad subject (and it is getting broader by the day). The subject is deemed difficult because one needs to spend some time (and a few hundred pages) of (demanding) abstract formalism before one gets to see some concrete applications. This is often frustrating and a beginner often looses sight of what is going on.

This beautiful book by Mumford was written sometime ago (when the standard Algebraic Geometry Textbooks of today were non-existent) and the abstract formalism of sheaves and schemes were still not textbook material (well EGA was available at that time I think!).
The book is written very clearly and informally and often Mumford tries to explain his point of view to the reader through simple but non-trivial examples. This is rather unique and I think it helps your understanding immensely.

The additional 1974 lectures themselves are worth the price of the book!

I will however add one small word of caution. The terminology in this book is little outdated and (in hindsight) non-standard. But that is no excuse to not try it!
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Format: Paperback Verified Purchase
This book is a must for any student in Algebraic Geometry or any student in Differential Geometry using algebraic techniques.
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Format: Paperback Verified Purchase
When I received this magnificent product, I found out that it was indeed a book. Moreover, I understand that it was indeed written by David Mumford. Upon opening it, I saw that it discusses varieties, and also that it discusses schemes.

However, the book fails to be as advertised in one key aspect: it is not red.
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