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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) [Paperback]

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Item description for The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians (Lecture Notes in Mathematics) by David Mumford...

Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all about.
This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry. The book is aimed at graduate students and professors seeking to learn
i) the concept of "scheme" as part of their study of algebraic geometry and
ii) an overview of moduli problems for curves and of the use of theta functions to study these.

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Item Specifications...

Pages   304
Est. Packaging Dimensions:   Length: 0.75" Width: 5.75" Height: 8.75"
Weight:   0.95 lbs.
Binding  Softcover
Release Date   Oct 29, 1999
Publisher   Springer
ISBN  354063293X  
ISBN13  9783540632931  

Availability  0 units.

More About David Mumford

Register your artisan biography and upload your photo! Biography of  David Mumford

David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.

Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.

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Reviews - What do customers think about The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians (Lecture Notes in Mathematics)?

The nearly Royal Road  Dec 10, 2001
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.

Probably none of these books will work for you unless you already know some algebraic geometry: how polynomials define a variety, the Zariski topology, what regular and birational maps are. There is more than enough in Myles Reid's humorously titled UNDERGRADUATE ALGEBRAIC GEOMETRY and UNDERGRADUATE COMMUTATIVE ALGEBRA with vividly geometric ideas in slightly scheme-theoretic language.

The RED BOOK now includes the Michigan lectures, which are reputedly terrific, but I have not worked through them.

Before Hartshorne  Dec 1, 1999
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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