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Real Algebraic Geometry

  • Book
  • © 1998

Overview

Authors:
  1. Jacek Bochnak

    1. Mathematisch Instituut, Vrije Universiteit, Amsterdam, The Netherlands

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  2. Michel Coste

    1. Institut Mathématique de Rennes, Université de Rennes 1, Rennes cedex, France

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  3. Marie-Françoise Roy

    1. Institut Mathématique de Rennes, Université de Rennes 1, Rennes cedex, France

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  • A systematic treatment of real algebraic geometry
  • Carefully and clearly written – may serve as a basis for a graduate course
  • Many of the new developments are included in this edition

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. Introduction

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 1-5

  3. Ordered Fields, Real Closed Fields

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 7-21

  4. Semi-algebraic Sets

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 23-58

  5. Real Algebraic Varieties

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 59-82

  6. Real Algebra

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 83-95

  7. The Tarski-Seidenberg Principle as a Transfer Tool

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 97-102

  8. Hilbert’s 17th Problem. Quadratic Forms in Real Algebraic Geometry

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 103-131

  9. Real Spectrum

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 133-160

  10. Nash Functions

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 161-206

  11. Stratifications

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 207-243

  12. Real Places

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 245-262

  13. Topology of Real Algebraic Varieties

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 263-296

  14. Algebraic Vector Bundles

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 297-337

  15. Polynomial or Regular Mappings with Values in Spheres

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 339-371

  16. Algebraic Models of C ∞ Manifolds

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 373-381

  17. Witt Rings in Real Algebraic Geometry

    • Jacek Bochnak, Michel Coste, Marie-Françoise Roy
    Pages 383-405

  18. Back Matter

    Pages 407-430
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Keywords

About this book

The present volume is a translation, revision and updating of our book (pub­lished in French) with the title "Géométrie Algébrique Réelle". Since its pub­lication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original.

Authors and Affiliations

  • Mathematisch Instituut, Vrije Universiteit, Amsterdam, The Netherlands

    Jacek Bochnak

  • Institut Mathématique de Rennes, Université de Rennes 1, Rennes cedex, France

    Michel Coste, Marie-Françoise Roy

Bibliographic Information

  • Book Title: Real Algebraic Geometry

  • Authors: Jacek Bochnak, Michel Coste, Marie-Françoise Roy

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-03718-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Hardcover ISBN: 978-3-540-64663-1Published: 19 August 1998

  • Softcover ISBN: 978-3-642-08429-4Published: 03 December 2010

  • eBook ISBN: 978-3-662-03718-8Published: 11 November 2013

  • Series ISSN: 0071-1136

  • Series E-ISSN: 2197-5655

  • Edition Number: 1

  • Number of Pages: X, 430

  • Additional Information: Title of the original French edition: Geometrie algebrique reelle: in the series Ergebnisse Mathematik 3. Folge volume 12

  • Topics: Algebraic Geometry

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