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Published January 1, 2019 | Version v1
Journal article Open

Real algebraic curves with large finite number of real points

Creators

  • 1. Univ Nantes, Lab Math Jean Leray, 2 Rue Houssiniere, F-44322 Nantes 3, France
  • 2. Bilkent Univ, Dept Math, TR-06800 Ankara, Turkey
  • 3. Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, 4 Pl Jussieu, F-75252 Paris 5, France
  • 4. Univ Angers, CNRS, Lab Angevin Rech Math LAREMA, F-49045 Angers 01, France

Description

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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