Building blocks of amplified endomorphisms of normal projective varieties

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 ∼ q H 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.