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A classical result of Boole shows that, in characteristic 0, the set ofsingular degree d hypersurfaces in P^N is a divisor of degree (N+1)(d-1)^N inthe projective space of all hypersurfaces. We give here analogous formulae forcomplete intersections in P^N of arbitrary codimension and degrees, in anycharacteristic.    Un resultat classique de Boole montre que, sur un corps de caracteristique 0,l'ensemble des hypersurfaces singulieres de degre d dans P^N est un diviseur dedegre (N+1)(d-1)^N de l'espace projectif de toutes les hypersurfaces. Onobtient ici des formules analogues pour des intersections completes decodimension et de degres quelconques dans P^N, en toute caracteristique.

Degr\'es d'homog\'en\'eit\'e de l'ensemble des intersections compl\`etes singuli\`eres