2025/07/08 by Caucher Birkar, Seung-Joo Lee, Birkar, Caucher +1 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2507.06317
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.