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  • Textbook
  • © 1999

The Red Book of Varieties and Schemes

Includes the Michigan Lectures (1974) on Curves and their Jacobians

Authors:

  • David Mumford's first work in schemes was established in the literature as the Red Book long before it was formally published.

  • It is still a standard, much-used reference on this subject.

  • As a result it has been reprinted several times.

  • This 2nd edition is augmented by another well-known, but now unavailable text of the author "Curves and their Jacobians" (62 pp)

  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1358)

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eBook USD 59.99
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  • ISBN: 978-3-540-46021-3
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  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 79.99
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Table of contents (7 chapters)

  1. Front Matter

    Pages N2-X
  2. I. Varieties

    • David B. Mumford
    Pages 1-63
  3. II. Preschemes

    • David B. Mumford
    Pages 65-136
  4. III. Local Properties of Schemes

    • David B. Mumford
    Pages 137-223
  5. Appendix: Curves and Their Jacobians

    • David B. Mumford
    Pages 225-291
  6. References: The Red Book of Varieties and Schemes

    • David B. Mumford
    Pages 293-293
  7. Back Matter

    Pages 307-311

About this book

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.

Keywords

  • Schottky problem
  • Theta functions
  • algebraic varieties
  • curves
  • schemes

Reviews

"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

Bibliographic Information

  • Book Title: The Red Book of Varieties and Schemes

  • Book Subtitle: Includes the Michigan Lectures (1974) on Curves and their Jacobians

  • Authors: David Mumford

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b62130

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-63293-1Published: 17 September 1999

  • eBook ISBN: 978-3-540-46021-3Published: 21 February 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 2

  • Number of Pages: X, 314

  • Topics: Algebraic Geometry

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-46021-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 79.99
Price excludes VAT (USA)