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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 ISSN 1073-7928.

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Official URL: https://doi.org/10.1093/imrn/rnv173

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > 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:
DateEvent
25 June 2015Published
7 May 2015Accepted
Volume: 2016
Number: 7
Page Range: pp. 2026-2067
DOI: 10.1093/imrn/rnv173
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): 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
Date of first compliant deposit: 9 October 2019
Date of first compliant Open Access: 14 October 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
FIRB 2012 Ministero dell’Istruzione, dell’Università e della Ricercahttp://dx.doi.org/10.13039/501100003407
Roth ScholarshipImperial College Londonhttp://dx.doi.org/10.13039/501100000761
DMS-0701101National Science Foundationhttp://dx.doi.org/10.13039/100000001
DMS-120065National Science Foundationhttp://dx.doi.org/10.13039/100000001
UNSPECIFIEDGruppo Nazionale per l'Analisi Matematica, la ProbabilitĂ  e le loro Applicazionihttp://dx.doi.org/10.13039/100012740
UNSPECIFIEDMax-Planck-Institut fĂĽr Mathematikhttp://viaf.org/viaf/127650144
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