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.
Codogni, G., Fanelli, A., Svaldi, R., Tasin, L. (2016). Fano Varieties in Mori Fibre Spaces. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016(7), 2026-2067 [10.1093/imrn/rnv173].
Fano Varieties in Mori Fibre Spaces
Codogni G.;
2016-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
