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

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arxiv 2507.06317 v1 pith:534Z2XXW submitted 2025-07-08 hep-th math.AG

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

classification hep-th math.AG
keywords boundpicardrankbasecalabi-yauellipticstrategysurfaces
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 5 Pith papers

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