K-polystable smooth Fano threefolds with ample Q-divisor polarization have reductive automorphism groups.
Matsushima,Sur la structure du groupe d’hom´ eomorphismes analytiques d’une certaine vari´ et´ e K¨ ahl´ erienne, Nagoya Mathematical Journal11(1957), 145–150
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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.