The g-periodic subvarieties for an automorphism g of positive entropy on a compact Kahler manifold

Details The g-periodic subvarieties for an automorphism g of positive entropy on a compact Kahler manifold The g-periodic subvarieties for an automorphism g of positive entropy on a compact Kahler manifold

2009-08-17

arxiv.org/abs/0908.2364v1

Mathematics

Algebraic Geometry

Advances in Mathematics (to appear), 11 pages

Scientific paper

For a compact Kahler manifold X and a strongly primitive automorphism g of positive entropy, it is shown that X has at most rank NS(X) of g-periodic prime divisors B_i (i.e., g^s(B_i) = B_i for some s > 0). When X is a projective threefold, every prime divisor containing infinitely many g-periodic curves, is shown to be g-periodic itself (a result in the spirit of the Dynamic Manin-Mumford conjecture).

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