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

Abstract

Using the Abban–Zhuang theory and the classification of 3-dimensional log smooth log Fano pairs due to Maeda, we prove that almost all threefold log Fano pairs [Formula: see text] of Maeda type with reducible boundary [Formula: see text] are K-unstable for any values of the boundary coefficients. We also correct several inaccuracies in Maeda’s classification.