Fujita decomposition and Massey product for fibered varieties

Abstract

Let $f:X\to B$ be a semistable fibration where $X$ is a smooth variety of dimension $n\ge 2$ 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 $f_{\ast }\ddot{I}{‰}_{X/B}$. 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 $B={\mathbb{P}}^1$.

29 pages