= Relative de Rham complex
{title2=$\Omega^\bullet_{\mathcal X/S},\ d_{\mathcal X/S}$}
For a holomorphic submersion, relative differential forms are forms modulo those containing a base differential. The relative exterior derivative gives a complex whose fibrewise hypercohomology is complex cohomology for a smooth proper family. Its filtration by degree defines the <Hodge filtration>; retaining exactly one base differential in the absolute complex constructs the <Gauss–Manin connection>.
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