4 problems

Isotriviality conjecture for minimal manifolds. If $S$ is minimal with $\dim S\geq 4$, then every fiber of $\pi$ is biholomorphic to $S$.

Let $f:X\to Y$ be a smooth projective family between complex quasi-projective manifolds. Assume that each fiber of $f$ has semi-ample canonical bundle, and that the Kobayashi pseud…

Let $f_U:U\to V$ be a smooth projective family, and suppose that $V$ has a morphism $\mu:V\to P_h$, where $P_h$ is the coarse moduli scheme associated with the moduli functor of po…

Let $f:X\to B$ be an algebraic smooth family of canonically polarised manifolds with generically maximal variation, and let $B$ be a special quasi-projective manifold, meaning that…