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

Twists of the Albanese varieties of cyclic multiple planes with large ranks over higher dimension function fields