Explicit biregular/birational geometry of affine threefolds: completions of A^3 into del Pezzo fibrations and Mori conic bundles

Adrien Dubouloz, Takashi Kishimoto

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 a…