Courbes rationnelles et droites en position générale
On montre que la réunion générale d’une courbe rationnelle avec des droites dans est de rang maximum.
Court’s conjecture on points in
Curves in P2(C) with 1-dimensional symmetry.
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...
Curves of genus 2 and Desargues configurations.
Curves on surfaces of degree 2r-... in Pr.
Cuspidal Projections of Space Curves.