Building blocks of amplified endomorphisms of normal projective varieties

Meng, Sheng

doi:10.1007/s00209-019-02316-7

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Building blocks of amplified endomorphisms of normal projective varieties

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Meng, Sheng
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00209-019-02316-7
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Citation

Meng, S. (2020). Building blocks of amplified endomorphisms of normal projective varieties. Mathematische Zeitschrift, 294(3-4), 1727-1747. doi:10.1007/s00209-019-02316-7.

Cite as: https://hdl.handle.net/21.11116/0000-0006-0C56-D

Abstract

Let $X$ be a normal projective variety. A surjective endomorphism $f:X\to X$
is int-amplified if $f^\ast L - L =H$ for some ample Cartier divisors $L$ and $H$. This is a generalization of the so-called polarized endomorphism which requires that $f^*H\sim qH$ 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.