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arXiv · 2507.06317

A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds

Caucher Birkar·Seung-Joo Lee
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Abstract

We compute an explicit rank bound on the Picard group of the compact surfaces, which can serve as the base of an elliptic Calabi-Yau variety with canonical singularities. To bound the Picard rank from above, we develop a novel strategy in birational geometry, motivated in part by the physics of six-dimensional vacua of F-theory as discussed in a companion paper [1] to this one. The derivation of the concrete bound illustrates the strategy and clarifies the origin of the boundedness.

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Caucher Birkar, Seung-Joo Lee. 2025-07-08. A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds. https://arxiv.org/abs/2507.06317

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