A sharp bound on the number of real intersection points of a sparse plane curve with a line. (July 2017) - Bihan, Frédéric; El Hilany, Boulos
Abstract: We prove that the number of real intersection points of a real line with a real plane curve defined by a polynomial with at most t monomials is either infinite or does not exceed 6 t − 7 . This improves a result by M. Avendaño. Furthermore, we prove that this bound is sharp for t = 3 with the help of Grothendieck's dessins d'enfant.