Title: Exceptional del Pezzo surfaces

Abstract: A sufficient condition for the existence
of a Kahler-Einstein metric on a Fano manifold can be
formulated in terms of so-called alpha-invariant of Tian.
This invariant can be naturally defined for log terminal
log Fano varieties and for a germ of log terminal singularity.
Using this invariant we prove the existence of Kahler-Einstein metrics
on many quasismooth well-formed weighted del Pezzo hypersurface
and compare this result with new obstructions found
by J.Gauntlett, D.Martelli, J.Sparks and S.-T.Yau.
We apply our technique to classify weakly-exceptional
quasismooth well-formed weighted del Pezzo hypersurface
using the classification of isolated rational quasihomogeneous
three-dimensional singularities obtained by S.S.T.Yau and Y.Yu.