Cylinders in del Pezzo fibrations |
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Authors: | Adrien Dubouloz Takashi Kishimoto |
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Institution: | 1.IMB UMR5584, CNRS, Université de Bourgogne Franche-Comté,Dijon,France;2.Department of Mathematics, Faculty of Science,Saitama University,Saitama,Japan |
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Abstract: | We show that a del Pezzo fibration π: V → W of degree d contains a vertical open cylinder, that is, an open subset whose intersection with the generic fiber of π is isomorphic to Z × AK1 for some quasi-projective variety Z defined over the function field K of W, if and only if d ≥ 5 and π: V → W admits a rational section. We also construct twisted cylinders in total spaces of threefold del Pezzo fibrations π: V → P1 of degree d ≤ 4. |
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