Mathematical Research Letters

Volume 17 (2010)

Number 5

Invariant Hypersurfaces in holomorphic Dynamics

Pages: 833 – 841



Serge Cantat (Université de Rennes 1, Campus de Beaulieu, F-35042 Rennes)


We prove the following result, which is analogous to two theorems, one due to Kodaira and Krasnov and another one due to Jouanolou and Ghys. Let $M$ be a compact complex manifold and $f$ a dominant endomorphism of $M.$ If there exist $k$ totally invariant irreducible hypersurfaces $W_i\subset M,$ with $k > \dim(M)+ h^{1,1}(M)$ then $f$ preserves a nontrivial meromorphic fibration. We then study the case where $f$ is a meromorphic map.

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