The movable cone of certain Calabi-Yau threefolds of Picard number two

Abstract

We describe explicitly the chamber structure of the movable cone for a general smooth complete intersection Calabi-Yau threefold $X$ of Picard number two in certain Pr-ruled Fano manifold and hence verify the Morrison-Kawamata cone conjecture for such $X$. Moreover, all birational minimal models of such Calabi-Yau threefolds are found, whose number is finite up to isomorphism.

arXiv comment42 pages. Correct some typos in this new version. Comments are welcome

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• On numerical dimensions of Calabi--Yau varieties
• The movable cone of Calabi--Yau threefolds in ruled Fano manifolds