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 "Géometrie algébrique réelle" 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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Editorial Reviews
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"Wie schon das französische Original, so ist auch die englische Version sehr sorgfältig verfasst. Beim Vergleich zwischen beiden stösst man immer wieder auf Stellen, wo der ursprüngliche Text nicht nur einfach übersetzt, sondern im Interesse einer noch klareren Darstellung auch neu konzipiert worden ist. Kein Zweifel, dass die neue Fassung auch weiterhin die Rolle einer Standradreferenz spielen wird."
DMV Jahresbericht, 103. Band, Heft 2, Juli 2001
DMV Jahresbericht, 103. Band, Heft 2, Juli 2001
Language Notes
Text: English (translation)
Original Language: French
Original Language: French
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Inside This Book
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First Sentence:
Abstract. The first three sections of this chapter briefly review Artin-Schreier theory: ordered fields, real fields, real closed fields and the real closure of an ordered field. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine real algebraic variety, real prime ideal, prime cone, nonsingular algebraic subset, stratifying family, global algebraic sections, affine real algebraic varieties, biregular isomorphism, nonsingular algebraic set, local conic structure, constructible topology, bilinear space, real closed extension, real valuation ring, arbitrary real closed field, topological vector bundle, real algebraic structure, real nullstellensatz, irreducible algebraic set, open hypercube, real algebraic sets, tilde operation, nonsingular bilinear forms, algebraic vector bundle, algebraic line bundle Key Phrases - Capitalized Phrases (CAPs): (learn more)
Henselian Properties, Hilbert's Theorem, Product of Spheres, Projection of Semi-algebraic Sets, Some Analysis New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Abstract. The first three sections of this chapter briefly review Artin-Schreier theory: ordered fields, real fields, real closed fields and the real closure of an ordered field. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine real algebraic variety, real prime ideal, prime cone, nonsingular algebraic subset, stratifying family, global algebraic sections, affine real algebraic varieties, biregular isomorphism, nonsingular algebraic set, local conic structure, constructible topology, bilinear space, real closed extension, real valuation ring, arbitrary real closed field, topological vector bundle, real algebraic structure, real nullstellensatz, irreducible algebraic set, open hypercube, real algebraic sets, tilde operation, nonsingular bilinear forms, algebraic vector bundle, algebraic line bundle Key Phrases - Capitalized Phrases (CAPs): (learn more)
Henselian Properties, Hilbert's Theorem, Product of Spheres, Projection of Semi-algebraic Sets, Some Analysis New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 2
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69
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- New York (Land of Liberty) by Ellen Sturm in Back Matter (1), Back Matter (2), and Back Matter (3)
- Algorithms in Real Algebraic Geometry by Denis S. Arnon in Back Matter
- Computer Algebra in Scientific Computing: 8th International Workshop, CASC 2005, Kalamata, Greece, September 12-16, 2005, Proceedings (Lecture Notes ... Computer Science and General Issues) by Victor G. Ganzha on 5 pages
- Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space (Porter Lectures) by Shmuel Weinberger on page 35, and page 92
- Positive Polynomials: From Hilbert's 17th Problem to Real Algebra (Springer Monographs in Mathematics) by Alexander Prestel in Back Matter (1), and Back Matter (2)
- Tame Topology and O-minimal Structures (London Mathematical Society Lecture Note Series) by L. P. D. van den Dries in Back Matter (1), and Back Matter (2)
- Real Analytic and Algebraic Singularities (Chapman & Hall/CRC Research Notes in Mathematics Series) by Toshisumi Fukui on page 28, and page 61
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