K-polystable smooth Fano threefolds with ample Q-divisor polarization have reductive automorphism groups.
Donaldson,Scalar curvature and stability of toric varieties, Journal of Differential Geometry62(2002), 289–349
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A Matsushima theorem for K-polystable polarised smooth Fano threefolds
K-polystable smooth Fano threefolds with ample Q-divisor polarization have reductive automorphism groups.