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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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https://hal.archives-ouvertes.fr/hal-01832739
Contributor : Frédéric Mangolte <>
Submitted on : Friday, January 18, 2019 - 6:46:54 PM
Last modification on : Saturday, April 11, 2020 - 1:57:57 AM

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

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