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arXiv · 2604.20440

A Matsushima theorem for K-polystable polarised smooth Fano threefolds

Hamid Abban·Paolo Cascini·Ivan Cheltsov
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Abstract

We prove that if $X$ is a smooth Fano threefold and $L$ is an ample $\mathbb{Q}$-divisor such that $(X,L)$ is K-polystable, then the automorphism group $\operatorname{Aut}(X)$ is reductive. This verifies the reductivity statement predicted by the Yau--Tian--Donaldson conjecture in the setting of smooth Fano threefolds with arbitrary ample polarisation.

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Hamid Abban, Paolo Cascini, Ivan Cheltsov. 2026-04-22. A Matsushima theorem for K-polystable polarised smooth Fano threefolds. https://arxiv.org/abs/2604.20440

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