Hirzebruch-Kummer covers of algebraic surfaces

Authors: PIOTR POKORA

Abstract: 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.

Keywords: Ball-quotients, Hirzebruch surfaces, surfaces of general type, Hirzebruch-Kummer covers, curve configurations

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