We show that being a general fibre of a Mori fibre space 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 three 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. (2015). Fano Varieties in Mori Fibre Spaces. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, rnv173 [10.1093/imrn/rnv173].
Fano Varieties in Mori Fibre Spaces
CODOGNI, GIULIO;Fanelli, Andrea;SVALDI, ROBERTO;
2015-01-01
Abstract
We show that being a general fibre of a Mori fibre space 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 three 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.
