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

Yusuke Kimura

doi:10.1093/ptep/pty039

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arXiv · 1801.06525

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

Yusuke Kimura

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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.

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Yusuke Kimura. 2018-01-19. K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications. https://doi.org/10.1093/ptep%2Fpty039

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