How to compute the alpha-invariant of Tian?
Ivan Cheltsov (University of Edinburgh)

A sufficient condition for the existence of an orbifold Kahler-Einstein metric
on a Fano orbifold can be formulated in terms of its global log canonical
threshold, which is an algebraic counterpart of the alpha-invariant of Tian.
For del Pezzo orbifolds this invariant must be strictly greater than 2/3 to
ensure the existence of an orbifold Kahler-Einstein metric.
In some cases this invariant can be easily computed, e.g. for toric Fano
orbifolds. But usually the global log canonical threshold is not easy to compute,
e.g. for smooth cubic surfaces. We show how to compute the global
log canonical thresholds of some well-formed quasismooth del Pezzo
hypersurfaces in weighted projective spaces.
This talk, intended more for specialists, will be preceded by a more general talk
at the conference "Kähler and Sasakian Geometry in Rome" (Galicki memorial)
on june 17 at 15:30 in Roma "La Sapienza". The latter talk is not required to
understand this one.

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