Building blocks of amplified endomorphisms of normal projective varieties

Sheng Meng

doi:10.1007/s00209-019-02316-7

Building blocks of amplified endomorphisms of normal projective varieties

Sheng Meng^*

^*此作品的通讯作者

National University of Singapore

科研成果: 期刊稿件 › 文章 › 同行评审

28 引用（Scopus）

摘要

Let X be a normal projective variety. A surjective endomorphism f: X→ X is int-amplified if f^∗L- L= H for some ample Cartier divisors L and H. This is a generalization of the so-called polarized endomorphism which requires that f^∗H∼ qH for some ample Cartier divisor H and q> 1. We show that this generalization keeps all nice properties of the polarized case in terms of the singularity, canonical divisor, and equivariant minimal model program.

源语言	英语
页（从-至）	1727-1747
页数	21
期刊	Mathematische Zeitschrift
卷	294
期	3-4
DOI	https://doi.org/10.1007/s00209-019-02316-7
出版状态	已出版 - 1 4月 2020
已对外发布	是

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abstract = "Let X be a normal projective variety. A surjective endomorphism f: X→ X is int-amplified if f∗L- L= H for some ample Cartier divisors L and H. This is a generalization of the so-called polarized endomorphism which requires that f∗H∼ qH for some ample Cartier divisor H and q> 1. We show that this generalization keeps all nice properties of the polarized case in terms of the singularity, canonical divisor, and equivariant minimal model program.",

keywords = "Albanese map, Albanese morphism, Amplified endomorphism, Equivariant MMP, Iteration, MRC fibration, Q-abelian variety",

author = "Sheng Meng",

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N2 - Let X be a normal projective variety. A surjective endomorphism f: X→ X is int-amplified if f∗L- L= H for some ample Cartier divisors L and H. This is a generalization of the so-called polarized endomorphism which requires that f∗H∼ qH for some ample Cartier divisor H and q> 1. We show that this generalization keeps all nice properties of the polarized case in terms of the singularity, canonical divisor, and equivariant minimal model program.

AB - Let X be a normal projective variety. A surjective endomorphism f: X→ X is int-amplified if f∗L- L= H for some ample Cartier divisors L and H. This is a generalization of the so-called polarized endomorphism which requires that f∗H∼ qH for some ample Cartier divisor H and q> 1. We show that this generalization keeps all nice properties of the polarized case in terms of the singularity, canonical divisor, and equivariant minimal model program.

KW - Albanese map

KW - Albanese morphism

KW - Amplified endomorphism

KW - Equivariant MMP

KW - Iteration

KW - MRC fibration

KW - Q-abelian variety

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Building blocks of amplified endomorphisms of normal projective varieties

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