Fubini–Study forms on punctured Riemann surfaces
In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We show that the quotient of the induced Fubini–Study forms by Kodaira maps of high tensor powers of the...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2025-06-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.763/ |
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| author | Apredoaei, Razvan Ma, Xiaonan Wang, Lei |
| author_facet | Apredoaei, Razvan Ma, Xiaonan Wang, Lei |
| author_sort | Apredoaei, Razvan |
| collection | DOAJ |
| description | In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We show that the quotient of the induced Fubini–Study forms by Kodaira maps of high tensor powers of the line bundle and the Poincaré form near the singularity grows polynomially uniformly on a neighborhood of the singularity as the tensor power tends to infinity, as an application of the method in [5]. |
| format | Article |
| id | doaj-art-f43b8ed7f8f34e04849eb9e42ca40da2 |
| institution | Matheson Library |
| issn | 1778-3569 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-f43b8ed7f8f34e04849eb9e42ca40da22025-08-01T07:26:12ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692025-06-01363G660361510.5802/crmath.76310.5802/crmath.763Fubini–Study forms on punctured Riemann surfacesApredoaei, Razvan0Ma, Xiaonan1Wang, Lei2Université Paris Cité, CNRS, IMJ-PRG, Bâtiment Sophie Germain, UFR de Mathématiques, Case 7012, 75205 Paris Cedex 13, FranceChern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. ChinaIn this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We show that the quotient of the induced Fubini–Study forms by Kodaira maps of high tensor powers of the line bundle and the Poincaré form near the singularity grows polynomially uniformly on a neighborhood of the singularity as the tensor power tends to infinity, as an application of the method in [5].https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.763/ |
| spellingShingle | Apredoaei, Razvan Ma, Xiaonan Wang, Lei Fubini–Study forms on punctured Riemann surfaces Comptes Rendus. Mathématique |
| title | Fubini–Study forms on punctured Riemann surfaces |
| title_full | Fubini–Study forms on punctured Riemann surfaces |
| title_fullStr | Fubini–Study forms on punctured Riemann surfaces |
| title_full_unstemmed | Fubini–Study forms on punctured Riemann surfaces |
| title_short | Fubini–Study forms on punctured Riemann surfaces |
| title_sort | fubini study forms on punctured riemann surfaces |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.763/ |
| work_keys_str_mv | AT apredoaeirazvan fubinistudyformsonpuncturedriemannsurfaces AT maxiaonan fubinistudyformsonpuncturedriemannsurfaces AT wanglei fubinistudyformsonpuncturedriemannsurfaces |