Building blocks of amplified endomorphisms of normal projective varieties

By Sheng Meng. Mathematische Zeitschrift, 2017

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Let X be a normal projective variety. A surjective endomorphism $$f{:}X\rightarrow X$$ f : X → X is int-amplified if $$f^*L - L =H$$ 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 $$f^*H\sim qH$$ f ∗ H ∼ q H for some ample Cartier divisor H and $$q>1$$ 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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df0971b50f573ab1149a60dd84205cb442712eb2