Kähler-Einstein Metrics On Log Del Pezzo Surfaces in Weighted Projective 3-Spaces [antikvár]

KAHLER-EINSTEIN METRICS ON LOG DEL PEZZO SURFACES IN WEIGHTED PROJECTIVE 3-SPACES by J. M. JOHNSON and J. KOLLÁR A log del Pezzo surface is a projective surface with quotient singularities such that its anticanonical class is ample. Such surfaces arise natúrally in many different contexts, for instance in connection with affine surfaces (Miyanishi [Mi]), moduli of surfaces of generál type (Alexeev [A12]), 3 and 4 dimensional minimai model program (Alexeev [Ali]). They alsó provide a natural testing ground for existence results of Káhler-Einstein metrics. The presence of quotient singularities forces us to work with orbifold metrics, but this is usually only a minor inconvenience. Log del Pezzo surfaces with a Káhler-Einstein metric alsó lead to Sasakian-Einstein 5-manifolds by Boyer-Galicki ([BoGa]). In connection with [DeKo], the authors ran a computer program to find examples of log del Pezzo surfaces in weighted project ive spaces. The program examined weights up to a few hundred and produced 3 examples of log del Pezzo surfaces where the methods of Demailly-Kollár ([DeKo], §6), proved the existence of a Káhler-Einstein metric. The aim of this paper is twofold. First, we determine the complete list of anticanonically embedded quasi smooth log del Pezzo surfaces in Keywords: Del Pezzo surface - Káhler-Einstein metric. Math. classifícation: 14J26 - 14Q10 - 32Q20.