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The greatest Ricci lower bound, conical Einstein metrics and the Chern number inequality
We partially confirm a conjecture of Donaldson relating the greatest Ricci
lower bound to the existence of conical Kahler-Einstein metrics on a
Fano manifold . In particular, if is a smooth simple divisor
and the Mabuchi -energy is bounded below, then there exists a unique conical
Kahler-Einstein metric satisfying for any
. We also construct unique smooth conical toric
Kahler-Einstein metrics with and a unique effective Q-divisor
for all toric Fano manifolds. Finally we prove a Miyaoka-Yau type
inequality for Fano manifolds with
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