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The Red Book of Varieties and Schemes

  • Book
  • © 1988

Overview

Authors:
  1. David Mumford

    1. Department of Mathematics, Harvard University, Cambridge, USA

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

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About this book

"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)

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Table of contents (28 chapters)

  1. Front Matter

    Pages N2-V
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  2. Varieties

    1. Front Matter

      Pages 1-1
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    2. Some algebra

      • David Mumford
      Pages 2-7

    3. Irreducible algebraic sets

      • David Mumford
      Pages 7-15

    4. Definition of a morphism: I

      • David Mumford
      Pages 15-24

    5. Sheaves and affine varieties

      • David Mumford
      Pages 24-35

    6. Definition of prevarieties and morphism

      • David Mumford
      Pages 35-45

    7. Products and the Hausdorff Axiom

      • David Mumford
      Pages 46-55

    8. Dimension

      • David Mumford
      Pages 56-67

    9. The fibres of a morphism

      • David Mumford
      Pages 67-75

    10. Complete varieties

      • David Mumford
      Pages 75-80

    11. Complex varieties

      • David Mumford
      Pages 80-89

  3. Preschemes

    1. Front Matter

      Pages 91-92
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    2. Spec (R)

      • David Mumford
      Pages 93-108

    3. The category of preschemes

      • David Mumford
      Pages 108-121

    4. Varieties are preschemes

      • David Mumford
      Pages 121-131

    5. Fields of definition

      • David Mumford
      Pages 131-142

    6. Closed subpreschemes

      • David Mumford
      Pages 143-155

    7. The functor of points of a prescheme

      • David Mumford
      Pages 155-167

    8. Proper morphisms and finite morphisms

      • David Mumford
      Pages 168-176
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Authors and Affiliations

  • Department of Mathematics, Harvard University, Cambridge, USA

    David Mumford

Bibliographic Information

  • Book Title: The Red Book of Varieties and Schemes

  • Authors: David Mumford

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-21581-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • eBook ISBN: 978-3-662-21581-4Published: 11 November 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: V, 315

  • Number of Illustrations: 13 b/w illustrations

  • Topics: Algebraic Geometry

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