We extend a generic vanishing result for flat unitary vector bundles from compact Kähler manifolds to manifolds in the Fujiki class \(\mathcal {C}\) . In particular, smooth proper complex algebraic varieties are covered. The proof relies on the Riemann–Hilbert correspondence, relating flat unitary vector bundles to unitary local systems. We review the Albanese morphism of regular manifolds, relaxing the usual Kähler condition. The result follows from Krämer–Weissauer’s vanishing theorem, applied to the derived direct image of the underlying unitary local system along the Albanese morphism.
