  In [17], we proved a structure theorem on the Mordell-Weil group of abelian
varieties over function fields that arise as the twists of abelian varieties by
the cyclic covers of projective varieties in terms of the Prym varieties
associated with covers. In this paper, we provide an explicit way to construct
the abelian varieties with large ranks over the higher dimension function
fields. To do so, we apply the above-mentioned theorem to the twists of
Albanese varieties of the cyclic multiple planes.
