Fubini–Study forms on punctured Riemann surfaces

Razvan Apredoaei; Xiaonan Ma; Lei Wang

doi:10.5802/crmath.763

Article de recherche - Analyse et géométrie complexes

Fubini–Study forms on punctured Riemann surfaces
[Formes de Fubini–Study sur des surfaces de Riemann épointées]

Razvan Apredoaei ¹ ; Xiaonan Ma ² ; Lei Wang ³

¹ Université Paris Cité, CNRS, IMJ-PRG, Bâtiment Sophie Germain, UFR de Mathématiques, Case 7012, 75205 Paris Cedex 13, France
² Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China
³ School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 603-615.

Abstract (VO)
Résumé

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].

Dans cet article, nous considérons une surface de Riemann épointée munie d’une métrique hermitienne qui coïncide avec la métrique de Poincaré près des points de ponction, ainsi qu’un fibré en droites holomorphe qui polarise la métrique. Nous montrons que le quotient des formes induites de Fubini–Study par les applications de Kodaira des puissances tensorielles élevées du fibré en droites et de la forme de Poincaré près de la singularité croît de manière polynomiale et uniforme dans un voisinage de la singularité lorsque la puissance tensorielle tend vers l’infini, en application de la méthode décrite dans [5].

Reçu le : 2025-02-14
Révisé le : 2025-05-22
Accepté le : 2025-06-02
Publié le : 2025-06-05

DOI : 10.5802/crmath.763

Affiliations des auteurs :

Razvan Apredoaei ¹ ; Xiaonan Ma ² ; Lei Wang ³

¹ Université Paris Cité, CNRS, IMJ-PRG, Bâtiment Sophie Germain, UFR de Mathématiques, Case 7012, 75205 Paris Cedex 13, France
² Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China
³ School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2025__363_G6_603_0,
     author = {Razvan Apredoaei and Xiaonan Ma and Lei Wang},
     title = {Fubini{\textendash}Study forms on punctured {Riemann} surfaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {603--615},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.763},
     language = {en},
}

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Razvan Apredoaei; Xiaonan Ma; Lei Wang. Fubini–Study forms on punctured Riemann surfaces. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 603-615. doi : 10.5802/crmath.763. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.763/

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