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

@article{Kimura2018K3SW,
title={K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications},
author={Y. Kimura},
journal={arXiv: High Energy Physics - Theory},
year={2018}
}

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.