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arXiv · 2610.01276

An elliptic Calabi-Yau threefold of Mordell-Weil rank twelve

Dominik Burek
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Abstract

We construct a smooth projective Calabi--Yau threefold with a flat elliptic fibration of Mordell--Weil rank twelve and Hodge numbers $(h^{1,1},h^{2,1})=(25,1)$. The construction starts from the Kummer surfaces associated with the products of a fixed elliptic curve and the level-four modular family. The threefold is birational to an anticanonical quartic in $\mathbb{P}(\mathcal{O}_{\mathbb{P}^1}(3)^{\oplus2}\oplus\mathcal{O}_{\mathbb{P}^1}(4)\oplus\mathcal{O}_{\mathbb{P}^1})$. We give twelve independent sections and construct a projective crepant resolution of the associated Weierstrass model.

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Dominik Burek. 2026-10-01. An elliptic Calabi-Yau threefold of Mordell-Weil rank twelve. https://arxiv.org/abs/2610.01276

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