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^*

^*Corresponding author for this work

National University of Singapore

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

28 Scopus citations

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.

Original language	English
Pages (from-to)	1727-1747
Number of pages	21
Journal	Mathematische Zeitschrift
Volume	294
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-019-02316-7
State	Published - 1 Apr 2020
Externally published	Yes

Keywords

Albanese map
Albanese morphism
Amplified endomorphism
Equivariant MMP
Iteration
MRC fibration
Q-abelian variety

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10.1007/s00209-019-02316-7

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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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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

UR - https://www.scopus.com/pages/publications/85065735977

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DO - 10.1007/s00209-019-02316-7

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VL - 294

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EP - 1747

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Building blocks of amplified endomorphisms of normal projective varieties

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Keywords

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