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Building blocks of amplified endomorphisms of normal projective varieties

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Abstract

Let X be a normal projective variety. A surjective endomorphism \(f{:}X\rightarrow X\) 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 \(f^*H\sim qH\) 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.

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Acknowledgements

The author would like to thank Professor De-Qi Zhang for many inspiring discussions, Professor Najmuddin Fakhruddin for providing Example 10.1, and the anonymous colleague for the suggestion of Example 10.2. He thanks the referee for very careful reading and many useful suggestions to revise this paper. He also thanks Max Planck Institute for Mathematics for providing an impressive acadamic environment. The author is supported by a Research Assistantship of the National University of Singapore.

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  1. Department of Mathematics, National University of Singapore, Singapore, 119076, Republic of Singapore

    Sheng Meng

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Meng, S. Building blocks of amplified endomorphisms of normal projective varieties. Math. Z. 294, 1727–1747 (2020). https://doi.org/10.1007/s00209-019-02316-7

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