On line and pseudoline configurations and ball-quotients

Jürgen Bokowski, Piotr Pokora

Abstract


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.


Keywords


Line configurations, Hirzebruch inequality, Melchior inequality, Shnurnikov inequality, ball-quotients

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications