Real algebraic geometry

Jacek Bochnak, Michel Coste, Marie-Françoise Roy

This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Geometrie algebrique reelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

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[目次]

  • 1. Ordered Fields, Real Closed Fields.- 2. Semi-algebraic Sets.- 3. Real Algebraic Varieties.- 4. Real Algebra.- 5. The Tarski-Seidenberg Principle as a Transfer Tool.- 6. Hilbert's 17th Problem. Quadratic Forms.- 7. Real Spectrum.- 8. Nash Functions.- 9. Stratifications.- 10. Real Places.- 11. Topology of Real Algebraic Varieties.- 12. Algebraic Vector Bundles.- 13. Polynomial or Regular Mappings with Values in Spheres.- 14. Algebraic Models of C? Manifolds.- 15. Witt Rings in Real Algebraic Geometry.- Index of Notation.

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この本の情報

書名 Real algebraic geometry
著作者等 Bochnak, J.
Coste, M.
Roy, M-F
Coste Michel
Roy Marie-Francoise
Bochnak Jacek
書名別名 Géométrie algébrique réelle
シリーズ名 Ergebnisse der Mathematik und ihrer Grenzgebiete
出版元 Springer
刊行年月 c1998
ページ数 ix, 430 p.
大きさ 25 cm
ISBN 3540646639
NCID BA37216791
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言語 英語
原文言語 フランス語
出版国 ドイツ
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