[The Togliatti type of varieties]
The Del Pezzo surface , 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, 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.
La surface de Del Pezzo de degré 6 obtenue par l'éclatement de trois points non alignés du plan projectif complexe (par le système linéaire des cubiques) possède une propriété spectaculaire : ses hyperplans osculateurs ont un point commun dans l'espace ambiant. Pour cette raison la surface est appelée surface de Togliatti. Nous donnons deux explications de ce phénomène. Nous en déduisons alors deux familles différentes de variétés possèdant une propriété analogue.
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Jean Vallès 1
@article{CRMATH_2006__343_6_411_0, author = {Jean Vall\`es}, title = {Vari\'et\'es de type {Togliatti}}, journal = {Comptes Rendus. Math\'ematique}, pages = {411--414}, publisher = {Elsevier}, volume = {343}, number = {6}, year = {2006}, doi = {10.1016/j.crma.2006.08.004}, language = {fr}, }
Jean Vallès. Variétés de type Togliatti. Comptes Rendus. Mathématique, Volume 343 (2006) no. 6, pp. 411-414. doi : 10.1016/j.crma.2006.08.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.08.004/
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[5] Alcuni esempi di superficie algebriche degli iperspazi che rappresentano un'equazione di Laplace, Comm. Math. Helv. I (1929), pp. 255-272
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