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Mathematics > Algebraic Geometry

arXiv:1805.05679 (math)
[Submitted on 15 May 2018]

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

Authors:Adrien Dubouloz (CNRS, IMB), 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.
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1805.05679 [math.AG]
  (or arXiv:1805.05679v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.05679

Submission history

From: Adrien Dubouloz [view email] [via CCSD proxy]
[v1] Tue, 15 May 2018 10:06:05 UTC (16 KB)
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