%0 Journal Article
%T Explicit biregular/birational geometry of affine threefolds: completions of A^3 into del Pezzo fibrations and Mori conic bundles
%A Adrien Dubouloz
%A Takashi Kishimoto
%J Mathematics
%D 2015
%I arXiv
%X We study certain pencils of del Pezzo surfaces generated by a smooth del Pezzo surface S of degree less or equal to 3 anti-canonically embedded into a weighted projective space P and an appropriate multiple of a hyperplane H. Our main observation is that every minimal model program relative to the morphism lifting such pencil on a suitable resolution of its indeterminacies preserves the open subset P \ H £¿ A^3. As an application, we obtain projective completions of A^3 into del Pezzo fibrations over P^1 of every degree less or equal to 4. We also obtain completions of A^3 into Mori conic bundles, whose restrictions to A^3 are twisted C*-fibrations over A^2 .
%U http://arxiv.org/abs/1508.01792v1