Variétés de type Togliatti

The Del Pezzo surface S 6 , obtained by blowing up the projective plane along three points (non aligned) has the following nice property: its osculating hyperplanes have a common point. For that reason, S 6 is also called the Togliatti surface. In this Note we give two explanations of this fact. From this we obtain two different families of varieties with an analogous property. To cite this article: J. Vallès, C. R. Acad. Sci. Paris, Ser. I 343 (2006).