A variation of Hodge structure of weight 
on a complex manifold 
consists of a rational local system 
and a decreasing filtration 
by holomorphic subbundles of 
. Every fiber is a Hodge
structure of weight 
, and the associated flat connection satisfies Griffiths transversality,
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A constant Hodge structure gives a constant variation (Huybrechts 2016). Families of smooth projective varieties supply geometric examples through their cohomology local systems.
