Geodesic
On line and pseudoline configurations and ball-quotients
Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 409-416.

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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.
DOI : 10.26493/1855-3974.1100.4a7
Keywords: Line configurations, Hirzebruch inequality, Melchior inequality, Shnurnikov inequality, ball-quotients 
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Jürgen Bokowski; Piotr Pokora. On line and pseudoline configurations and ball-quotients. Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 409-416. doi : 10.26493/1855-3974.1100.4a7. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1100.4a7/

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