K-stability of log Fano threefolds of Maeda type

Log smooth log Fano threefolds with integral boundary were classified by H. Maeda in 1986. Unlike “classical” Fano varieties, they are not bounded. Recently, K. Fujita introduced a class of log Fano varieites of Maeda type, which provides a natural playground for the study of K-stability of log Fano pairs (or, log K-stability). It turns out that, in the case of reducible boundary, in dimension 3 such pairs are K-unstable, with finitely many exceptions. We will discuss this result.