Mordell-Weil ranks of isotrivial abelian varieties over function fields and fundamental groups of discriminants

I will describe a relation between
the ranks in the title in the case
of abelian varieties over the field of
complex rational functions in two variables
and Alexander invariants of the fundamental
group of the discriminant. The main step is a description of Albanese varieties of some cyclic covers of plane as a products of abelian varieties of CM type corresponding to cyclotomic fields.