Kähler-Einstein metrics for some quasi-smooth log del Pezzo surfaces

Abstract

Recently Johnson and Kollár determined the complete list of anticanonically embedded quasi-smooth log del Pezzo surfaces in weighted projective 3 3 -spaces. They also proved that many of those surfaces admit a Kähler-Einstein metric, and that some of them do not have tigers. The aim of this paper is to settle the question of the existence of Kähler-Einstein metrics and tigers for those surfaces for which the question was left open. In order to do so, we will use techniques developed earlier by Nadel, Demailly and Kollár.