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Journal Articles European Journal of Mathematics Year : 2019

Real algebraic curves with large finite number of real points

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.
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Dates and versions

hal-01832739 , version 1 (08-07-2018)
hal-01832739 , version 2 (18-01-2019)

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Cite

Erwan Brugallé, Alex Degtyarev, Ilia Itenberg, Frédéric Mangolte. Real algebraic curves with large finite number of real points. European Journal of Mathematics, 2019, 5, pp.686-711. ⟨10.1007/s40879-019-00324-9⟩. ⟨hal-01832739v2⟩
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