Among the notes never published by the late Prof. E.G.Togliatti one can find an interesting collection of questions and one of these is the extension of the theory of inflection points of elliptic cubics to cubic primals in a projective space of dimension greater than 3. This study is in line with that of F.E.Eckardt concerning the inflection points (later called Eckardt's points) of a cubic surface in ordinary 3-dimensional space, that is, nonsingular points which are the intersection of three lines lying on the surface. The general cubic hypersurface has no inflection points, and in this paper we find the maximum possible number of inflection points for a nonsingular cubic hypersurface of Pn.
Inflection points of cubic hypersurfaces
CANONERO, GABRIELLA;CATALISANO, MARIA VIRGINIA;SERPICO, MARIA EZIA
1997-01-01
Abstract
Among the notes never published by the late Prof. E.G.Togliatti one can find an interesting collection of questions and one of these is the extension of the theory of inflection points of elliptic cubics to cubic primals in a projective space of dimension greater than 3. This study is in line with that of F.E.Eckardt concerning the inflection points (later called Eckardt's points) of a cubic surface in ordinary 3-dimensional space, that is, nonsingular points which are the intersection of three lines lying on the surface. The general cubic hypersurface has no inflection points, and in this paper we find the maximum possible number of inflection points for a nonsingular cubic hypersurface of Pn.
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