# A Tower of Riemann Surfaces whose Bergman Kernels Jump at the Roof

### Takeo Ohsawa

Nagoya University, Nagoya, Chikusa-Ku, Japan

## Abstract

It is shown that, for any Fuchsian group $Γ$ acting on the complex upper half plane $H$ such that $H/Γ$ is a compact hyperelliptic Riemann surface, there exists a sequence of subgroups $Γ_{n}⊂Γ(n=1,2,…)$ satisfying $Γ_{1}=Γ$ and $⋂_{n=1}Γ_{n}={id}$ such that the associated sequence of the Bergman kernels of $H/Γ_{n}$, pulled back to $H$, does not converge to the Bergman kernel of $H$.

## Cite this article

Takeo Ohsawa, A Tower of Riemann Surfaces whose Bergman Kernels Jump at the Roof. Publ. Res. Inst. Math. Sci. 46 (2010), no. 3, pp. 473–478

DOI 10.2977/PRIMS/14