JournalsprimsVol. 46, No. 3pp. 473–478

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

  • Takeo Ohsawa

    Nagoya University, Nagoya, Chikusa-Ku, Japan
A Tower of Riemann Surfaces whose Bergman Kernels Jump at the Roof cover
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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