Comptes Rendus
no. 7
Complex analysis/Analytic geometry
Boundary asymptotics of the relative Bergman kernel metric for elliptic curves
[Asymptotique au bord de la métrique du noyau de Bergman relatif pour des courbes elliptiques]

Présenté par : Jean-Pierre Demailly

Robert Xin Dong1, 2
1 Department of Mathematics, Tongji University, Shanghai 200092, China
2 Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 611-615.

Pour une famille de surfaces de Riemann compactes, nous étudions les comportements asymptotiques de la métrique du noyau relatif de Bergman à proximité des frontières des espaces de modules. Nous montrons que la métrique du noyau relatif de Bergman sur une famille de courbes elliptiques a une croissance hyperbolique au point singulier. La preuve est principalement basée sur la théorie des fonctions elliptiques.

For a family of compact Riemann surfaces, we study the asymptotic behaviors of the relative Bergman kernel metric near the boundaries of the moduli spaces. We have shown that the relative Bergman kernel metric on a family of elliptic curves has hyperbolic growth at the node. The proof relies largely on the elliptic function theory.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.04.015
Robert Xin Dong 1, 2

1 Department of Mathematics, Tongji University, Shanghai 200092, China
2 Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan 
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Robert Xin Dong. Boundary asymptotics of the relative Bergman kernel metric for elliptic curves. Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 611-615. doi : 10.1016/j.crma.2015.04.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.015/

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