Overview
Issu d’un cours de maîtrise de l’Université Paris VII, ce texte est réédité tel qu’il était paru en 1978. A propos du théorème de Bézout sont introduits divers outils nécessaires au développement de la notion de multiplicité d’intersection de deux courbes algébriques dans le plan projectif complexe. Partant des notions élémentaires sur les sous-ensembles algébriques affines et projectifs, on définit les multiplicités d’intersection et interprète leur somme entermes du résultant de deux polynômes. L’étude locale est prétexte à l’introduction des anneaux de série formelles ou convergentes ; elle culmine dans le théorème de Puiseux dont la convergence est ramenée par des éclatements à celle du théorème des fonctions implicites. Diverses figures éclairent le texte: on y ""voit"" en particulier que l’équation homogène x3+y3+z3 = 0 définit un tore dans le plan projectif complexe.
Full Product Details
Author: Alain Chenciner
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 1ière ed. 1978. 2ième tirage 2007
Dimensions:
Width: 15.50cm
, Height: 1.00cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9783540337072
ISBN 10: 3540337075
Pages: 160
Publication Date: 18 October 2007
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of stock
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Language: French
Reviews
From the reviews: The book contains an introduction to the theory of algebraic plane curves, in a form suitable for a first course in Algebraic Geometry at undergraduate/graduate level. Using the basic properties of polynomial rings, the author introduces algebraic sets in the plane, irreducible components and local analysis by means of localisations of the coordinate rings. the author presents the local theory of singularities and intersection multiplicities, using as his basic tool the Puiseux expansions at a point. (Luca Chiantini, Zentralblatt MATH, Vol. 1133 (11), 2008)
From the reviews: The book contains an introduction to the theory of algebraic plane curves, in a form suitable for a first course in Algebraic Geometry at undergraduate/graduate level. ... Using the basic properties of polynomial rings, the author introduces algebraic sets in the plane, irreducible components and local analysis by means of localisations of the coordinate rings. ... the author presents the local theory of singularities and intersection multiplicities, using as his basic tool the Puiseux expansions at a point. (Luca Chiantini, Zentralblatt MATH, Vol. 1133 (11), 2008)
From the reviews: <p> The book contains an introduction to the theory of algebraic plane curves, in a form suitable for a first course in Algebraic Geometry at undergraduate/graduate level. a ] Using the basic properties of polynomial rings, the author introduces algebraic sets in the plane, irreducible components and local analysis by means of localisations of the coordinate rings. a ] the author presents the local theory of singularities and intersection multiplicities, using as his basic tool the Puiseux expansions at a point. (Luca Chiantini, Zentralblatt MATH, Vol. 1133 (11), 2008)
Author Information
Sous-ensembles algébriques de C.- Ensembles algébriques affines.- Courbes planes affines.- Ensembles algébriques projectifs.- Courbes projectives planes : le théorème de Bezout.- Le résultant.- Point de vue local : anneaux de series formelles.- Anneaux de series convergentes.- Le théorème de Puiseux.- Théorie locale des intersections de courbes.
