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By Boyer Ch. P.

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Additional info for 3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients

Sample text

Supposons X ^ W. Alors (cf. 2) il existe /

C'est cette constatation qui conduit a la notion de faisceau. 1. a. 1. Soit X un espace topologique et soit K un ensemble. Un faisceau de fonctions sur X a valeurs dans K est la donnee pour tout ouvert U de X d'un ensemble J-"(U) de fonctions definies sur U et a valeurs dans K, avec les deux axiomes suivants : 1) Restriction : Si V est un ouvert inclus dans U et si f € F(U), on afveF(V). 2) Recollement : Si U est reconvert par des ouverts Ui (i € /) et si 012 se donne des fa e F(Ui) telles que f^u^Uj = fj\UinUj, U existe une et une seule fonction f e F(U) telle que f\ui = fi.

Une variete algebrique affine est un espace annele isomorphe a un espace annele (V, Oy), ou V est un ensemble algebrique affine et Oy le faisceau des fonctions regulieres sur V. Un morphisme de varietes algebriques affines est simplement un morphisme d'espaces anneles. 2 a) Les auteurs americains reservent en general le mot variete au cas irreductible. e. independantes d'un plongement dans kn. 3. Soient V un ensemble algebrique affine et f € F(V). L'ouvert D(f], muni du faisceau Oy restreint a D(f), est une variete algebrique affine.

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