Smooth proper family of compact complex manifolds
= Smooth proper family of compact complex manifolds
{title2=$f:\mathcal X\to S$}
A proper holomorphic submersion has compact smooth fibres, and the <Ehresmann fibration theorem> gives differentiable local trivializations. Their integral cohomology, modulo torsion, forms a <local system>. If the fibres are <Kähler manifolds>, their Hodge filtrations form holomorphic subbundles and give a <variation of Hodge structure>. Properness is needed for this usual conclusion.