A Note on plane rational curves and the associated Poncelet Surfaces
We consider the parametrization (f0, f1, f2) of plane rational curve c, and we want to relate the splitting type of C (i.e. the second Betti numbers of the ideal (f0, f1, f2) with the singularities of the associated Poncelet surface in p3. We are able of doing this for Ascenzi curves, thus generalizing a result in  in the case of plane curves. Moreover we prove that if the Poncelet surface s C p3 is singular then it is associated with a curve C which possesses at least a point of multiplicity >_ 3.
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
EUT Edizioni Università di Trieste