Non-isomorphic endomorphisms of Fano threefolds

Sheng Meng; De Qi Zhang; Guolei Zhong

doi:10.1007/s00208-021-02274-8

Non-isomorphic endomorphisms of Fano threefolds

Sheng Meng
, De Qi Zhang
, Guolei Zhong^*

^*此作品的通讯作者

Korea Institute for Advanced Study
National University of Singapore

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

Let X be a smooth Fano threefold. We show that X admits a non-isomorphic surjective endomorphism if and only if X is either a toric variety or a product of P¹ and a del Pezzo surface; in this case, X is a rational variety. We further show that X admits a polarized (or amplified) endomorphism if and only if X is a toric variety.

源语言	英语
页（从-至）	1567-1596
页数	30
期刊	Mathematische Annalen
卷	383
期	3-4
DOI	https://doi.org/10.1007/s00208-021-02274-8
出版状态	已出版 - 8月 2022
已对外发布	是

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abstract = "Let X be a smooth Fano threefold. We show that X admits a non-isomorphic surjective endomorphism if and only if X is either a toric variety or a product of P1 and a del Pezzo surface; in this case, X is a rational variety. We further show that X admits a polarized (or amplified) endomorphism if and only if X is a toric variety.",

keywords = "Equivariant minimal model program, Fano threefold, Int-amplified endomorphism, Polarized endomorphism, Toric variety",

author = "Sheng Meng and Zhang, \{De Qi\} and Guolei Zhong",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Meng, Sheng

AU - Zhang, De Qi

AU - Zhong, Guolei

PY - 2022/8

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N2 - Let X be a smooth Fano threefold. We show that X admits a non-isomorphic surjective endomorphism if and only if X is either a toric variety or a product of P1 and a del Pezzo surface; in this case, X is a rational variety. We further show that X admits a polarized (or amplified) endomorphism if and only if X is a toric variety.

AB - Let X be a smooth Fano threefold. We show that X admits a non-isomorphic surjective endomorphism if and only if X is either a toric variety or a product of P1 and a del Pezzo surface; in this case, X is a rational variety. We further show that X admits a polarized (or amplified) endomorphism if and only if X is a toric variety.

KW - Equivariant minimal model program

KW - Fano threefold

KW - Int-amplified endomorphism

KW - Polarized endomorphism

KW - Toric variety

UR - https://www.scopus.com/pages/publications/85116321801

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JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Non-isomorphic endomorphisms of Fano threefolds

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