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

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	1567-1596
Number of pages	30
Journal	Mathematische Annalen
Volume	383
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-021-02274-8
State	Published - Aug 2022
Externally published	Yes

Keywords

Equivariant minimal model program
Fano threefold
Int-amplified endomorphism
Polarized endomorphism
Toric variety

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10.1007/s00208-021-02274-8

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title = "Non-isomorphic endomorphisms of Fano threefolds",

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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T1 - Non-isomorphic endomorphisms of Fano threefolds

AU - Meng, Sheng

AU - Zhang, De Qi

AU - Zhong, Guolei

PY - 2022/8

Y1 - 2022/8

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

U2 - 10.1007/s00208-021-02274-8

DO - 10.1007/s00208-021-02274-8

M3 - 文章

AN - SCOPUS:85116321801

SN - 0025-5831

VL - 383

SP - 1567

EP - 1596

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Non-isomorphic endomorphisms of Fano threefolds

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Keywords

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