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arXiv · 1805.05679

Cylinders in Mori Fiber Spaces: forms of the quintic del Pezzo threefold

Adrien Dubouloz·Takashi Kishimoto
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Abstract

Motivated by the general question of existence of open A1-cylinders in higher dimensional pro-jective varieties, we consider the case of Mori Fiber Spaces of relative dimension three, whose general closed fibers are isomorphic to the quintic del Pezzo threefold V5 , the smooth Fano threefold of index two and degree five. We show that the total spaces of these Mori Fiber Spaces always contain relative A2-cylinders, and we characterize those admitting relative A3-cylinders in terms of the existence of certain special lines in their generic fibers.

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Adrien Dubouloz, Takashi Kishimoto. 2018-05-15. Cylinders in Mori Fiber Spaces: forms of the quintic del Pezzo threefold. https://arxiv.org/abs/1805.05679

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