Building blocks of amplified endomorphisms of normal projective varieties

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.