Work

Varieties Admitting Polarized Galois Endomorphisms

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.05248

Authors: Jiang, Zhiyuan, Luo, Yujie

Institutions: University of Science and Technology of China, Purdue University West Lafayette

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220742461

Cites: 3

Cited by:

Related to: 10