On Standard Projective Plane Bundles Original Research Article

For aK-formVKofP2over the function fieldKover an algebraically closed fieldkof char(k) = 0, we will construct a proper flat surjective morphism τ: V → XwithVandXsmooth projective varieties overksuch that (i) the function field ofXisK, (ii) the generic fibre of τ is isomorphic toVK, (iii) the relative Picard number is equal to one. This is a generalization of a result of V. G. Sarkisov about standard conic bundles.