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Fano varieties in Mori fibre spaces
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Codogni, Giulio, Fanelli, Andrea, Svaldi, Roberto and Tasin, Luca (2015) Fano varieties in Mori fibre spaces. International Mathematics Research Notices, 2016 (7). pp. 2026-2067. doi:10.1093/imrn/rnv173
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Official URL: https://doi.org/10.1093/imrn/rnv173
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.
| Item Type: | Journal Article | |||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||
| Divisions: | Faculty of Science > Mathematics | |||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Geometry, Algebraic, Algebraic varieties, Homogeneous spaces | |||||||||||||||||||||
| Journal or Publication Title: | International Mathematics Research Notices | |||||||||||||||||||||
| Publisher: | Oxford University Press | |||||||||||||||||||||
| ISSN: | 1073-7928 | |||||||||||||||||||||
| Official Date: | 25 June 2015 | |||||||||||||||||||||
| Dates: |
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| Volume: | 2016 | |||||||||||||||||||||
| Number: | 7 | |||||||||||||||||||||
| Page Range: | pp. 2026-2067 | |||||||||||||||||||||
| DOI: | 10.1093/imrn/rnv173 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Publisher Statement: | This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Giulio Codogni, Andrea Fanelli, Roberto Svaldi, Luca Tasin, Fano Varieties in Mori Fibre Spaces, International Mathematics Research Notices, Volume 2016, Issue 7, 2016, Pages 2026–2067, https://doi.org/10.1093/imrn/rnv173 is available online at: https://doi.org/10.1093/imrn/rnv173 | |||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
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