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Comptes Rendus Mathématique
Volume 353, n° 7
pages 611-615 (juillet 2015)
Doi : 10.1016/j.crma.2015.04.015
Received : 22 August 2014 ;  accepted : 23 April 2015
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
 

Robert Xin Dong a, b
a Department of Mathematics, Tongji University, Shanghai 200092, China 
b Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan 

Abstract

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.

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Résumé

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.

The full text of this article is available in PDF format.


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