2014/12/03 by Dervan, Ruadhaí
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1412.1426
We give a criterion for the coercivity of the Mabuchi functional for general Kähler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the existence of a Kähler-Einstein metric. We also prove the alpha invariant is a continuous function on the Kähler cone. As an application, we provide new Kähler classes on a general degree one del Pezzo surface for which the Mabuchi functional is coercive.