Cylinders in del Pezzo fibrations

2016/07/04 by Dubouloz, Adrien, Kishimoto, Takashi · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.00840

Abstract

We show that a del Pezzo fibration π : V → W of degre d contains a vertical open cylinder, that is, an open subset whose intersection with the generic fiber of π is isomorphic to Z×\mathbbA_K¹ 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 → P 1 of degree d ≤ 4.

Cited by

• Cylindricity of weighted singular del Pezzo surfaces over fields of characteristic zero
• Automorphism groups and cylindricity of weighted hypersurface Fano threefolds

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