2019/01/21 by Meng, Sheng
#08A35 #11G10 #14E30 #14J50 #32H50 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1901.07089
Let X be a klt projective variety with numerically trivial canonical divisor. A surjective endomorphism f:X→ X is amplified (resp.~quasi-amplified) if f^*D-D is ample (resp.~big) for some Cartier divisor D. We show that after iteration and equivariant birational contractions, an quasi-amplified endomorphism will descend to an amplified endomorphism. As an application, when X is Hyperkähler, f is quasi-amplified if and only if it is of positive entropy. In both cases, f has Zariski dense periodic points. When X is an abelian variety, we give and compare several cohomological and geometric criteria of amplified endomorphisms and endomorphisms with countable and Zariski dense periodic points (after an uncountable field extension).