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arXiv · 1605.00757

On line and pseudoline configurations and ball-quotients

Jürgen Bokowski·Piotr Pokora
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Abstract

In this note we show that there are no real configurations of $d\geq 4$ lines in the projective plane such that the associated Kummer covers of order $3^{d-1}$ are ball-quotients and there are no configurations of $d\geq 4$ lines such that the Kummer covers of order $4^{d-1}$ are ball-quotients. Moreover, we show that there exists only one configuration of real lines such that the associated Kummer cover of order $5^{d-1}$ is a ball-quotient. In the second part we consider the so-called topological $(n_{k})$-configurations and we show, using Shnurnikov's inequality, that for $n < 27$ there do not exist $(n_{5})$-configurations and and for $n < 41$ there do not exist $(n_{6})$-configurations.

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Jürgen Bokowski, Piotr Pokora. 2016-05-03. On line and pseudoline configurations and ball-quotients. https://doi.org/10.26493/1855-3974.1100.4a7

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