Acta Mathematica Vietnamica
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Normal Projective Varieties Admitting Polarized or Int-amplified Endomorphisms
Sheng Meng
,
De-Qi Zhang
Abstract
Let X be a normal projective variety admitting a polarized or int-amplified endomorphism f. We list up characteristic properties of such an endomorphism and classify such a variety from the aspects of its singularity, anti-canonical divisor, and Kodaira dimension. Then, we run the equivariant minimal model program with respect to not just the single f but also the monoid SEnd(X) of all surjective endomorphisms of X, up to finite-index. Several applications are given. We also give both algebraic and geometric characterizations of toric varieties via polarized endomorphisms.