Caractérisations de l'espace projectif (conjectures de Hartshorne et de Frankel)
On montre que la réunion générale d’une courbe rationnelle avec des droites dans est de rang maximum.
In a previous paper we showed that the existence of a 1-parameter symmetry group of a hypersurface X in projective space was equivalent to failure of versality of a certain unfolding. Here we study in detail (reduced) plane curves of degree d ≥ 3, excluding the trivial case of cones. We enumerate all possible group actions -these have to be either semisimple or unipotent- for any degree d. A 2-parameter group can only occur if d = 3. Explicit lists of singularities of the corresponding curves are...