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Research article - Complex analysis and geometry, Algebraic geometry
An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves
Turgay Bayraktar1 ; Emel Karaca2
1 Faculty of Engineering and Natural Sciences, Sabancı University, İstanbul, 34956 Turkey
2 Polatlı Faculty of Science and Arts, Ankara Hacı Bayram Veli University, Ankara, 06900 Turkey
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 779-788.

We prove that maximal real algebraic curves associated with sub-Gaussian random real holomorphic sections of a smoothly curved ample line bundle are exponentially rare. This generalizes the result of Gayet and Welschinger [13] proved in the Gaussian case for positively curved real holomorphic line bundles.

Nous démontrons que les courbes algébriques réelles maximales associées aux sections holomorphes réelles sous-Gaussiennes d’un faisceau de lignes amples à courbure lisse sont exponentiellement raréfiées. Cela généralise le résultat de Gayet et Welschinger [13] ont prouvé dans le cas Gaussien des faisceaux de lignes holomorphes réels à courbure positive.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.596

Turgay Bayraktar 1; Emel Karaca 2

1 Faculty of Engineering and Natural Sciences, Sabancı University, İstanbul, 34956 Turkey
2 Polatlı Faculty of Science and Arts, Ankara Hacı Bayram Veli University, Ankara, 06900 Turkey
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     journal = {Comptes Rendus. Math\'ematique},
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Turgay Bayraktar; Emel Karaca. An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 779-788. doi : 10.5802/crmath.596. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.596/

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