We study a secondary operation (Massey product) associated to a variation of Hodge structure of complex algebraic curves.

The Fujita decomposition of fibered surfaces is the splitting of the 1.0-relative Hodge bundle into a sum of a locally trivial unitary bundle and a positive vector bundle.

We show that the vanishing of the Massey product implies that the monodromy of the unitary part of the Fujita decomposition is finite.

The result is joint work with Sara Torelli.