Abstract:
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.
