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Courbes Algébriques Planes
Paperback
ISBN13: 9783540337072
Publisher: Springer
Published: Oct 18 2007
Pages: 160
Weight: 0.61
Height: 0.40 Width: 6.10 Depth: 9.30
Language: French
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.
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