Abstract
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.
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