The Kawaguchi-Silverman conjecture is proved for projective bundles over abelian varieties or smooth projective varieties of Picard number one, via new structure theorems for endomorphisms of Fano contractions.
Advances in the equivariant minimal model program and their applications in complex and arithmetic dynamics
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This note reports some advances in the Equivariant Minimal Model Program (EMMP) for non-isomorphic surjective endomorphisms and their applications in complex and arithmetic dynamics.
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Dynamical Iitaka theory on Fano contractions
The Kawaguchi-Silverman conjecture is proved for projective bundles over abelian varieties or smooth projective varieties of Picard number one, via new structure theorems for endomorphisms of Fano contractions.