Cohomologically hyperbolic endomorphisms of complex manifolds

Details Cohomologically hyperbolic endomorphisms of complex manifolds Cohomologically hyperbolic endomorphisms of complex manifolds

2008-05-27

arxiv.org/abs/0805.4140v1

Mathematics

Dynamical Systems

International Journal of Mathematics (to appear)

Scientific paper

We show that if a compact Kahler manifold X admits a cohomologically
hyperbolic surjective endomorphism then its Kodaira dimension is non-positive.
This gives an affirmative answer to a conjecture of Guedj in the holomorphic
case. The main part of the paper is to determine the geometric structure and
the fundamental groups (up to finite index) for those X of dimension 3.

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