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On the Back Cover
Issu d un cours de maitrise de l Universite Paris VII, ce texte est reedite tel qu il etait paru en 1978. A propos du theoreme de Bezout sont introduits divers outils necessaires au developpement de la notion de multiplicite d intersection de deux courbes algebriques dans le plan projectif complexe. Partant des notions elementaires sur les sous-ensembles algebriques affines et projectifs, on definit les multiplicites d intersection et interprete leur somme entermes du resultant de deux polynomes. L etude locale est pretexte a l introduction des anneaux de serie formelles ou convergentes; elle culmine dans le theoreme de Puiseux dont la convergence est ramenee par des eclatements a celle du theoreme des fonctions implicites. Diverses figures eclairent le texte: on y "voit" en particulier que l equation homogene x3+y3+z3 = 0 definit un tore dans le plan projectif complexe."
About the Author
Sous-ensembles algA(c)briques de C.- Ensembles algA(c)briques affines.- Courbes planes affines.- Ensembles algA(c)briques projectifs.- Courbes projectives planes: le thA(c)orA]me de Bezout.- Le rA(c)sultant.- Point de vue local: anneaux de series formelles.- Anneaux de series convergentes.- Le thA(c)orA]me de Puiseux.- ThA(c)orie locale des intersections de courbes.
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