Hello.

I am finding some nontrivial examples of surjective holomorphic selfmap of compact Kahler manifold of dim $\geq 3$. That is, find $X$ a compact Kahler manifold of dim $\geq 3$, $f:X->X$ a surjective holomorphic selfmap so that:

1. X is not a projective space.

2. $f$ is not a submersion (or etale ?)

3. f has positive entropy.

4. f is not a product map.

References or nonexistence results are also welcome.

Thank you very much.