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Varieties Admitting Polarized Galois Endomorphisms
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≅ Pn. As another application, we prove that such X is of log Calabi-Yau type as conjectured by Gongyo.
Related
- Positivity of compact Kähler varieties admitting an int-amplified endomorphism
- Galois module structure of Deligne--Lusztig varieties for GL3
- Existence of Ulrich bundles on polarized surfaces and weakly Ulrich bundles on polarized varieties in positive characteristic
- Automorphisms of hypersurfaces in polarized varieties
- Projective Lifting Theorem, Complex Reflection Groups, and Quasi-Galois Points for Fermat Varieties
BibTeX
@misc{jiang2026varieties,
title = {{Varieties Admitting Polarized Galois Endomorphisms}},
author = {Zhiyuan Jiang and Yujie Luo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05248},
eprint = {2610.05248},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05248},
}
RIS
TY - UNPB
TI - Varieties Admitting Polarized Galois Endomorphisms
AU - Zhiyuan Jiang
AU - Yujie Luo
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05248
UR - https://arxiv.org/abs/2610.05248
AB - 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≅ P^n. As another application, we prove that such X is of log Calabi-Yau type as conjectured by Gongyo.
ER -