Exceptional del Pezzo hypersurfaces

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in P(a(0), a(1), a(2), a(3)). As a corollary we obtain the existence of orbifold Kahler-Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted hypersurfaces in P(a(0), a(1), a(2), a(3)).