Codogni, GiulioFanelli, AndreaSvaldi, RobertoTasin, Luca2018-12-132018-12-132018-12-132018-09-0110.1007/s40879-018-0219-zhttps://infoscience.epfl.ch/handle/20.500.14299/152579WOS:000444210700010We consider the problem of determining which Fano manifolds can be realised as fibres of a Mori fibre space. In particular, we study the case of toric varieties, Fano manifolds with high index and some Fano manifolds with high Picard rank.Mathematicsfano varietiesmori fibre spacestoric varietiesvertex-transitive polytopeshigh indexhigh picard rankfano manifoldsminimal modelschar pclassificationexistence3-foldsbundlestext::journal::journal article::research article