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Fano Varieties in Mori Fibre Spaces

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Codogni, G 
Fanelli, A 
Tasin, L 

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.

Description

Keywords

math.AG, math.AG, 14E30 14J45 14J26 14J30 14M25 14M15

Journal Title

International Mathematics Research Notices

Conference Name

Journal ISSN

1073-7928
1687-0247

Volume Title

2016

Publisher

Oxford University Press (OUP)