The arithmeticity of a Kodaira fibration is determined by its universal cover

Gabino González-Diez; Sebastián Reyes-Carocca

doi:10.4171/cmh/359

JournalscmhVol. 90, No. 2pp. 429–434

The arithmeticity of a Kodaira fibration is determined by its universal cover

Gabino González-Diez
Universidad Autónoma de Madrid, Spain
Sebastián Reyes-Carocca
Universidad Autónoma de Madrid, Spain

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Abstract

Let $S \to C$ be a Kodaira fibration. Here we show that whether or not the algebraic surface $S$ is defined over a number field depends only on the biholomorphic class of its universal cover.

Cite this article

Gabino González-Diez, Sebastián Reyes-Carocca, The arithmeticity of a Kodaira fibration is determined by its universal cover. Comment. Math. Helv. 90 (2015), no. 2, pp. 429–434

DOI 10.4171/CMH/359