Log Calabi-Yau Structure of Projective Threefolds Admitting Polarized Endomorphisms

Sheng Meng

doi:10.1093/imrn/rnac308

Log Calabi-Yau Structure of Projective Threefolds Admitting Polarized Endomorphisms

Sheng Meng^*

^*此作品的通讯作者

数学科学学院

Korea Institute for Advanced Study

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

Let X be a normal projective variety admitting a polarized endomorphism f, that is, f *H ∼ qH for some ample divisor H and integer q > 1. It was conjectured by Broustet and Gongyo that X is of Calabi.Yau type, that is, (X, Δ) is lc for some effective Q-divisor such that K_X + Δ ∼ _Q 0. In this paper, we establish a general guideline based on the equivariant minimal model program and the canonical bundle formula. In this way, we prove the conjecture when X is a smooth projective threefold.

源语言	英语
页（从-至）	21272-21289
页数	18
期刊	International Mathematics Research Notices
卷	2023
期	24
DOI	https://doi.org/10.1093/imrn/rnac308
出版状态	已出版 - 1 12月 2023

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AB - Let X be a normal projective variety admitting a polarized endomorphism f, that is, f *H ∼ qH for some ample divisor H and integer q > 1. It was conjectured by Broustet and Gongyo that X is of Calabi.Yau type, that is, (X, Δ) is lc for some effective Q-divisor such that KX + Δ ∼ Q 0. In this paper, we establish a general guideline based on the equivariant minimal model program and the canonical bundle formula. In this way, we prove the conjecture when X is a smooth projective threefold.

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Log Calabi-Yau Structure of Projective Threefolds Admitting Polarized Endomorphisms

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