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On certain rigid fibered Calabi-Yau threefolds. (English) Zbl 0852.14012

In the classification of fibered Calabi-Yau threefolds, there naturally appears a class of fibered Calabi-Yau threefolds called of type \(\text{II}_0 \text{A}\). This is by definition an elliptic fibered Calabi-Yau threefold whose base surface is a log Enriques surface of abelian type. This class is the most peculiar class of fibered Calabi-Yau threefolds. In this paper, we completely determine all the fibered Calabi-Yau threefolds of type \(\text{II}_0 \text{A}\) up to isomorphism as fiber spaces via studying flop phenomena associated with these threefolds. An explicit description of the representatives is also given.
Reviewer: K.Oguiso (Tokyo)

MSC:

14J30 \(3\)-folds
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32C99 Analytic spaces
14D99 Families, fibrations in algebraic geometry
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