Abstract. We consider the parametrization (f_0; f_1; f_2) of a 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) in K[P1] ) with the singularities of the associ- ated Poncelet surface in P3. We are able of doing this for Ascenzi curves, thus generalizing a result in [ISV] in the case of plane curves. Moreover we prove that if the Poncelet surfaces S in P3 is singular then it is associated to a curve C which possesses a point of multiplicity at least 3.
Bernardi, A., Ida', M., Gimigliano, A. (2015). A note on plane rational curves and associated Poncelet surfaces. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, 47, 59-64 [10.13137/0049-4704/11219].
A note on plane rational curves and associated Poncelet surfaces.
BERNARDI, ALESSANDRA;IDA', MONICA;GIMIGLIANO, ALESSANDRO
2015
Abstract
Abstract. We consider the parametrization (f_0; f_1; f_2) of a 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) in K[P1] ) with the singularities of the associ- ated Poncelet surface in P3. We are able of doing this for Ascenzi curves, thus generalizing a result in [ISV] in the case of plane curves. Moreover we prove that if the Poncelet surfaces S in P3 is singular then it is associated to a curve C which possesses a point of multiplicity at least 3.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
