# 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 Γ1 = 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