We show that being a general fibre of a Mori fibre space (MFS) is a rather restrictive condition for a Fano variety. More specifically, we obtain two criteria (one sufficient and one necessary) for a ℚ-factorial Fano variety with terminal singularities to be realised as a fibre of a Mori fibre space, which turn into a characterisation in the rigid case. We apply our criteria to figure out this property up to dimension 3 and on rational homogeneous spaces. The smooth toric case is studied and an interesting connection with K-semistability is also investigated.

Fano Varieties in Mori Fibre Spaces / G. Codogni, A. Fanelli, R. Svaldi, L. Tasin. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2016:7(2016), pp. 2026-2067.

Fano Varieties in Mori Fibre Spaces

R. Svaldi
;
L. Tasin
2016

Abstract

We show that being a general fibre of a Mori fibre space (MFS) is a rather restrictive condition for a Fano variety. More specifically, we obtain two criteria (one sufficient and one necessary) for a ℚ-factorial Fano variety with terminal singularities to be realised as a fibre of a Mori fibre space, which turn into a characterisation in the rigid case. We apply our criteria to figure out this property up to dimension 3 and on rational homogeneous spaces. The smooth toric case is studied and an interesting connection with K-semistability is also investigated.
Mathematics (all)
Settore MAT/03 - Geometria
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/638168
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