The aim of this paper is to show that using some natural curve arrangements in algebraic surfaces and Hirzebruch-Kummer covers, one cannot construct new examples of ball-quotients, i.e. minimal smooth complex projective surfaces of general type satisfying equality in the Bogomolov-Miyaoka-Yau inequality.
Ball-quotients, Hirzebruch surfaces, surfaces of general type, Hirzebruch-Kummer covers, curve configurations
"Hirzebruch-Kummer covers of algebraic surfaces,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 33.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/33