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Israel Journal of Mathematics

, Volume 225, Issue 2, pp 797–815 | Cite as

Cylinders in del Pezzo fibrations

  • Adrien DuboulozEmail author
  • Takashi Kishimoto
Article

Abstract

We show that a del Pezzo fibration π: VW 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: VW admits a rational section. We also construct twisted cylinders in total spaces of threefold del Pezzo fibrations π: VP1 of degree d ≤ 4.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.IMB UMR5584, CNRS, Université de Bourgogne Franche-ComtéDijonFrance
  2. 2.Department of Mathematics, Faculty of ScienceSaitama UniversitySaitamaJapan

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