On standard projective plane bundles

[摘要] For a K-form V-K of P-2 over the function field K over an algebraically closed field k of char(k) = 0, we will construct a proper flat surjective morphism tau:V --> X with V and X smooth projective varieties over k such that (i) the function field of X is K, (ii) the generic fibre of tau is isomorphic to V-K, (iii) the relative Picard number is equal to one. This is a generalization of a result of V. G. Sarkisov about standard conic bundles. (C) 1997 Academic Press.

[发布日期] 1997-11-01