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Article de recherche - Analyse et géométrie complexes, Géométrie algébrique
An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves
[Un résultat de raréfaction exponentielle pour les courbes algébriques maximales réelles sous-Gaussiennes]
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.

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.

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.

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {An {Exponential} {Rarefaction} {Result} for {Sub-Gaussian} {Real} {Algebraic} {Maximal} {Curves}},
     journal = {Comptes Rendus. Math\'ematique},
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     publisher = {Acad\'emie des sciences, Paris},
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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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