Real algebraic curves with large finite number of real points
Algebraic Geometry
2019-09-13 v1
Abstract
We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close to optimal curves of small degree. Our upper bound is sharp if the genus is small as compared to the degree. Some of the results are extended to other real algebraic surfaces, most notably ruled.
Cite
@article{arxiv.1807.03992,
title = {Real algebraic curves with large finite number of real points},
author = {Erwan Brugallé and Alex Degtyarev and Ilia Itenberg and Frédéric Mangolte},
journal= {arXiv preprint arXiv:1807.03992},
year = {2019}
}