Title: Fano Varieties in Mori Fibre Spaces
Speaker: Giulio Codogni, Roma Tre University
Seminar Type: Algebraic Geometry
Abstract: We show that being a general fibre of a Mori fibre space is a rather restrictive condition for a Fano variety. In order to detect this property, we obtain two criteria (one sufficient and one necessary) for a Q-factorial Fano variety with rational singularities to be realised as a fibre of a Mori fibre space, which turn into a characterisation in the rigid case. As an application, we apply our criteria to solve the classically known smooth two-dimensional case, give an almost exhaustive answer for smooth threefolds and flag varieties and a further characterisation on the polytope in the Gorenstein toric case. An interesting connection with K-semistability is also investigated. Joint work with A. Fanelli, R. Svaldi and L. Tasin.
