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The Morrison-Kawamata cone conjecture and abundance on Ricci flat manifolds. (English) Zbl 1409.32010
Ji, Lizhen (ed.) et al., Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations. Based on the conference, Institute Mittag-Leffler, Stockholm, Sweden, July 13–18, 2015. Somerville, MA: International Press; Beijing: Higher Education Press. Adv. Lect. Math. (ALM) 42, 157-185 (2018).
Summary: The aim of this survey is threefold: (a) to discuss the status of the Morrison-Kawamata cone conjecture, (b) to report on recent developments towards the Abundance Conjecture, and (c) to discuss the nef line bundle version of the Abundance Conjecture on $$K$$-trivial varieties.
For the entire collection see [Zbl 1398.14003].

##### MSC:
 32J27 Compact Kähler manifolds: generalizations, classification 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14J45 Fano varieties 32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
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