It is a classical result, first established by de Jonquières (1859), that generically the number of conics tangent to 5 given conics in the complex projective plane is 3264. We show here the existence of configurations of 5 real conics such that the number of real conics tangent to them is 3264.
@article{urn:eudml:doc:44276, title = {The number of conics tangent to five given conics: the real case.}, journal = {Revista Matem\'atica de la Universidad Complutense de Madrid}, volume = {10}, year = {1997}, pages = {391-421}, zbl = {0921.14036}, mrnumber = {MR1605670}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44276} }
Ronga, Felice; Tognoli, Alberto; Vust, Thierry. The number of conics tangent to five given conics: the real case.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 391-421. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44276/