F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces

Abstract

We constructed several families of elliptic K3 surfaces with Mordell-Weil groups of ranks from 1 to 4. We studied F-theory compactifications on these elliptic K3 surfaces times a K3 surface. Gluing pairs of identical rational elliptic surfaces with nonzero Mordell-Weil ranks yields elliptic K3 surfaces, the Mordell-Weil groups of which have nonzero ranks. The sum of the ranks of the singularity type and the Mordell-Weil group of any rational elliptic surface with a global section is 8. By utilizing this property, families of rational elliptic surfaces with various nonzero Mordell-Weil ranks can be obtained by choosing appropriate singularity types. Gluing pairs of these rational elliptic surfaces yields families of elliptic K3 surfaces with various nonzero Mordell-Weil ranks. We also determined the global structures of the gauge groups that arise in F-theory compactifications on the resulting K3 surfaces times a K3 surface. $U(1)$ gauge fields arise in these compactifications.

25 pages

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• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• Orders of Vanishing and U(1) Charges in F-theory
• $\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s
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• A note on transition in discrete gauge groups in F-theory
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