K-polystability of 3-dimensional log Fano pairs of Maeda type

Abstract

Using the Abban-Zhuang theory and the classification of three-dimensional log smooth log Fano pairs due to Maeda, we prove that threefold log Fano pairs $(X,D)$ of Maeda type with reducible boundary $D$ are K-unstable, with four exceptions. We also correct several inaccuracies in Maeda's classification.