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arXiv · 2610.05248

Varieties Admitting Polarized Galois Endomorphisms

Zhiyuan Jiang·Yujie Luo
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Abstract

Let $X$ be an $n$-dimensional smooth complex projective variety admitting an int-amplified Galois endomorphism. We prove that its maximal rationally connected fibration is represented by a smooth toric fibration over a smooth $Q$-abelian variety. Consequently, if $X$ is rationally connected, then it is toric. If it also has Picard number one, then $X\cong \mathbf{P}^n$. As another application, we prove that such $X$ is of log Calabi-Yau type as conjectured by Gongyo.

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Zhiyuan Jiang, Yujie Luo. 2026-10-04. Varieties Admitting Polarized Galois Endomorphisms. https://arxiv.org/abs/2610.05248

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