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

TL;DR

This paper constructs genus-one fibered K3 surfaces without a global section as double covers of Halphen surfaces, and explores their implications for F-theory compactifications with specific gauge and discrete symmetries.

Contribution

It introduces a novel method of constructing K3 surfaces without sections via double covers of Halphen surfaces, expanding the understanding of F-theory models.

Findings

K3 surfaces with $I_{n}$ fibers and bisection geometry

F-theory models with $SU(n)$ gauge symmetry and $bZ_2$ discrete symmetry

New examples of genus-one fibered K3 surfaces without sections

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.