A sharp bound on the number of real intersection points of a sparse plane curve with a line

2015/06/10 by Bihan, Frédéric, Hilany, Boulos El
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.03309

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 6t -7. This improves a result by M. Avendano. Furthermore, we prove that this bound is sharp for t = 3 with the help of Grothendieck's dessins d'enfant.

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