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^*

^*Corresponding author for this work

Korea Institute for Advanced Study
National University of Singapore

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

Access to Document

10.1007/s00208-021-02274-8

Cite this

@article{27e417195f18458baaebb1d662e4028a,

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.",

year = "2022",

month = aug,

doi = "10.1007/s00208-021-02274-8",

language = "英语",

volume = "383",

pages = "1567--1596",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this