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

TL;DR

This paper proves that most three-dimensional log Fano pairs of Maeda type with reducible boundary are K-unstable, correcting previous classification inaccuracies and identifying four exceptions.

Contribution

It establishes K-unstability for a broad class of threefold log Fano pairs of Maeda type, refining Maeda's classification with corrections.

Findings

Most Maeda type pairs are K-unstable

Four exceptions where pairs are not K-unstable

Corrections to Maeda's classification

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.