Fano varieties in Mori fibre spaces
Algebraic Geometry
2016-06-09 v2
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.
Keywords
Cite
@article{arxiv.1406.7634,
title = {Fano varieties in Mori fibre spaces},
author = {Giulio Codogni and Andrea Fanelli and Roberto Svaldi and Luca Tasin},
journal= {arXiv preprint arXiv:1406.7634},
year = {2016}
}
Comments
32 pages. Results on threefolds and rational homogeneous spaces strengthened. Result on toric varieties corrected. To appear in IMRN