3 problems

Let $S$ be a smooth irreducible quasi-projective variety over $\mathbb C$, let $K$ be a positive integer, and let $\Phi:S\times\mathbb P^K\to S\times\mathbb P^K$ be a family given…

Let $S$ be a smooth and irreducible quasi-projective variety over $\mathbb C$, let $N$ be a positive integer, and let $\Phi:S\times\mathbb P^N\to S\times\mathbb P^N$ be an algebrai…

Let $f:X\to X$ be a polarized endomorphism of a smooth projective variety over a field of characteristic zero, and let $Z\subset X$ be a subvariety containing a Zariski dense set o…