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arXiv · 2607.27048

On the boundedness of elliptic Calabi-Yau 4-folds

Stefano Filipazzi·Fulin Xu
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Abstract

In this work, we settle the boundedness of a vast class of elliptic Calabi-Yau 4-folds. In particular, we show that any elliptic Calabi-Yau 4-fold that is not crepant to the quotient of a product $Y \times E$, where $E$ is an elliptic curve and $Y$ a Calabi-Yau 3-fold, belongs to finitely many algebraic families. In particular, the statement applies whenever the elliptic fibration of the Calabi-Yau 4-fold is not isotrivial. We also provide partial evidence for the boundedness of the middle Betti number of Calabi-Yau 3-folds and study the index of fibered $K$-trivial 4-folds.

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Stefano Filipazzi, Fulin Xu. 2026-07-29. On the boundedness of elliptic Calabi-Yau 4-folds. https://arxiv.org/abs/2607.27048

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