In this note we show that there are no real configurations of d ≥ 4 lines in the projective plane such that the associated Kummer covers of order 3d − 1 are ball-quotients and there are no configurations of d ≥ 4 lines such that the Kummer covers of order 4d − 1 are ball-quotients. Moreover, we show that there exists only one configuration of real lines such that the associated Kummer cover of order 5d − 1 is a ball-quotient. In the second part we consider the so-called topological (nk)-configurations and we show, using Shnurnikov’s inequality, that for n < 27 there do not exist (n5)-configurations and and for n < 41 there do not exist (n6)-configurations.
@article{1100,
title = {On line and pseudoline configurations and ball-quotients},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {14},
year = {2017},
doi = {10.26493/1855-3974.1100.4a7},
language = {EN},
url = {http://dml.mathdoc.fr/item/1100}
}
Bokowski, Jürgen; Pokora, Piotr. On line and pseudoline configurations and ball-quotients. ARS MATHEMATICA CONTEMPORANEA, Tome 14 (2017) . doi : 10.26493/1855-3974.1100.4a7. http://gdmltest.u-ga.fr/item/1100/