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On the boundedness of elliptic Calabi-Yau 4-folds

2026/07/29 by Stefano Filipazzi, Fulin Xu
Mathematics · #math.AG #msc:14D06 #msc:14E30 #msc:14J27 #msc:14J32

paper · pdf

30 pages. Comments are welcome!

arxiv created 2026/07/29 · arxiv updated 2026/07/30

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 × 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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