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Mathematics  2001 

K?hler-Einstein Metrics for some quasi smooth log del Pezzo Surfaces

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Abstract:

Recently Johnson and Koll\'ar determined the complete list of anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. They also proved that many of those surfaces admit a K\"ahler-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 K\"ahler-Einstein metrics and tigers for those surfaces for which the question was still open. In order to do so, we will use techniques developed earlier by Nadel and Demailly and Koll\'ar.

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