Dynamics of automorphisms on projective complex manifolds

Details Dynamics of automorphisms on projective complex manifolds Dynamics of automorphisms on projective complex manifolds

2008-10-26

arxiv.org/abs/0810.4675v1

Mathematics

Algebraic Geometry

Journal of Differential Geometry, to appear

Scientific paper

We show that the dynamics of automorphisms on all projective complex manifolds X (of dimension 3, or of any dimension but assuming the Good Minimal Model Program or Mori's Program) are canonically built up from the dynamics on just three types of projective complex manifolds: complex tori, weak Calabi-Yau manifolds and rationally connected manifolds. As a by-product, we confirm the conjecture of Guedj for automorphisms on 3-dimensional projective manifolds, and also determine pi_1(X).

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