Elliptic Calabi–Yau 4-folds not crepant to a product quotient of a Calabi–Yau 3-fold times an elliptic curve form a bounded family.
The movable fan of the Horrocks-Mumford quintic
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abstract
This paper explores the birational geometry of a general Horrocks-Mumford quintic threefold, describing the set of all minimal models up to marked isomorphism, the movable fan (the way in which the nef cones of all these models are arranged to form the movable cone), and the birational automorphism group. There are infinitely many models up to marked isomorphism, falling into just eight (unmarked-) isomorphism classes.
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On the boundedness of elliptic Calabi-Yau 4-folds
Elliptic Calabi–Yau 4-folds not crepant to a product quotient of a Calabi–Yau 3-fold times an elliptic curve form a bounded family.