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

Adrien Dubouloz (1, 2) , Takashi Kishimoto (3)

1 CNRS - Centre National de la Recherche Scientifique
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 Department of Mathematics, Faculty of Science, Saitama University

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.

Mots clés: Fano threefold; Mori Fiber Space; Sarkisov link; Cremona involutions; Cylinders.

Domaines: Géométrie algébrique [math.AG]

Adrien Dubouloz, Takashi Kishimoto. Cylinders in Mori Fiber Spaces: forms of the quintic del Pezzo threefold . 2018. ⟨hal-01790674⟩