An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves
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 b...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.596/ |
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| _version_ | 1825206237066690560 |
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| author | Bayraktar, Turgay Karaca, Emel |
| author_facet | Bayraktar, Turgay Karaca, Emel |
| author_sort | Bayraktar, Turgay |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6f8213c589f34249b846c74f83c68bce |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-6f8213c589f34249b846c74f83c68bce2025-02-07T11:22:28ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-09-01362G777978810.5802/crmath.59610.5802/crmath.596An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal CurvesBayraktar, Turgay0Karaca, Emel1Faculty of Engineering and Natural Sciences, Sabancı University, İstanbul, 34956 TurkeyPolatlı Faculty of Science and Arts, Ankara Hacı Bayram Veli University, Ankara, 06900 TurkeyWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.596/ |
| spellingShingle | Bayraktar, Turgay Karaca, Emel An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves Comptes Rendus. Mathématique |
| title | An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves |
| title_full | An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves |
| title_fullStr | An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves |
| title_full_unstemmed | An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves |
| title_short | An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves |
| title_sort | exponential rarefaction result for sub gaussian real algebraic maximal curves |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.596/ |
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