[Asymptotique au bord de la métrique du noyau de Bergman relatif pour des courbes elliptiques]
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.
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@article{CRMATH_2015__353_7_611_0,
author = {Dong, Robert Xin},
title = {Boundary asymptotics of the relative {Bergman} kernel metric for elliptic curves},
journal = {Comptes Rendus. Math\'ematique},
pages = {611--615},
publisher = {Elsevier},
volume = {353},
number = {7},
year = {2015},
doi = {10.1016/j.crma.2015.04.015},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2015.04.015/}
}
TY - JOUR AU - Dong, Robert Xin TI - Boundary asymptotics of the relative Bergman kernel metric for elliptic curves JO - Comptes Rendus. Mathématique PY - 2015 SP - 611 EP - 615 VL - 353 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2015.04.015/ DO - 10.1016/j.crma.2015.04.015 LA - en ID - CRMATH_2015__353_7_611_0 ER -
%0 Journal Article %A Dong, Robert Xin %T Boundary asymptotics of the relative Bergman kernel metric for elliptic curves %J Comptes Rendus. Mathématique %D 2015 %P 611-615 %V 353 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2015.04.015/ %R 10.1016/j.crma.2015.04.015 %G en %F CRMATH_2015__353_7_611_0
Dong, Robert Xin. Boundary asymptotics of the relative Bergman kernel metric for elliptic curves. Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 611-615. doi : 10.1016/j.crma.2015.04.015. http://archive.numdam.org/articles/10.1016/j.crma.2015.04.015/
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