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© 1999

The Red Book of Varieties and Schemes

Second, Expanded Edition. Includes Michigan Lectures (1974) on Curves and their Jacobians

  • Authors
Textbook

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

Table of contents

  1. Front Matter
    Pages N2-X
    PDF
  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. Guide to the Literature and References: Curves and Their Jacobians
    David B. Mumford
    Pages 294-300
  8. Supplementary Bibliography on the Schottky Problem
    Enrico Arbarello
    Pages 301-304
  9. Back Matter
    Pages 307-311
    PDF

About this book

Introduction

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

Bibliographic information

  • Book Title The Red Book of Varieties and Schemes
  • Book Subtitle Second, Expanded Edition. Includes Michigan Lectures (1974) on Curves and their Jacobians
  • Authors David Mumford
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI https://doi.org/10.1007/b62130
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-63293-1
  • eBook ISBN 978-3-540-46021-3
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 2
  • Number of Pages X, 314
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
  • Buy this book on publisher's site

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