A sharp bound on the number of real intersection points of a sparse plane curve with a line
Algebraic Geometry
2015-06-11 v1
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.
Keywords
Cite
@article{arxiv.1506.03309,
title = {A sharp bound on the number of real intersection points of a sparse plane curve with a line},
author = {Frédéric Bihan and Boulos El Hilany},
journal= {arXiv preprint arXiv:1506.03309},
year = {2015}
}
Comments
10 pages, 1 Figure