FUJITA DECOMPOSITION and MASSEY PRODUCT for FIBERED VARIETIES

Let f: X → B be a semistable fibration where X is a smooth variety of dimension n ≥ 2 and B is a smooth curve. We give the structure theorem for the local system of the relative 1-forms and of the relative top forms. This gives a neat interpretation of the second Fujita decomposition of f∗ωX/B. We apply our interpretation to show the existence, up to base change, of higher irrational pencils and on the finiteness of the associated monodromy representations under natural Castelnuovo-type hypothesis on local subsystems. Finally, we give a criterion to have that X is not of Albanese general type if B= P1.