Intermediate Jacobians of projective plane bundles over a smooth projective surface

Let V → X be a standard P^2-bundle (Definition below) over a smooth projective surface X with the discriminant locus △ and the associated cyclic cover φ : △^^~ → △ of degree three. The purpose of this paper is (i) to determine the etale l-adic cohomology groups of V (Theorem A), (ii) to give an isomorphism of the intermediate jacobian of V and the Prym variety associated to the triple cover φ as polarized abelian varieties (Theorem B), and (iii) to show the existence of a standard P^2-bundle for a given cyclic cover of degree three over a normal crossing curve on X (Theorem D), under certain conditions of (X, △). An ideal basis of a standard P^2-bundle over a regular local ring is determined (Theorem E)