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Mathematics > Algebraic Geometry

arXiv:1807.03992 (math)
[Submitted on 11 Jul 2018]

Title:Real algebraic curves with large finite number of real points

Authors:Erwan Brugallé (LMJL), Alex Degtyarev, Ilia Itenberg (IMJ-PRG), Frédéric Mangolte (LAREMA)
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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.
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1807.03992 [math.AG]
  (or arXiv:1807.03992v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.03992
Journal reference: European Journal of Mathematics, 5 (2019), no. 3, 686--711
Related DOI: https://doi.org/10.1007/s40879-019-00324-9

Submission history

From: Frederic Mangolte [view email] [via CCSD proxy]
[v1] Wed, 11 Jul 2018 08:24:54 UTC (192 KB)
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