K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications

Abstract

We construct several examples of genus-one fibered K3 surfaces without a global section with type $I_n$ fibers, by considering double covers of a special class of rational elliptic surfaces lacking a global section, known as Halphen surfaces of index 2. The resulting K3 surfaces have bisection geometries. F-theory compactifications on these K3 genus-one fibrations without a section times a K3 yield models that have $SU(n)$ gauge symmetries with a discrete ${\mathbb{Z}}_2$ symmetry.

18 pages. Some clarifications and updated references

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Cited by in corpus (6)

• Discrete gauge groups in certain F-theory models in six dimensions
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• Explicit Constructions of Halphen Pencils