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

Yusuke Kimura

doi:10.1093/ptep/pty039

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

High Energy Physics - Theory 2018-04-24 v2 Algebraic Geometry

Authors: 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.

Keywords

K3 surfaces genus-one fibration Halphen surfaces double covers F-theory gauge symmetry

Cite

@article{arxiv.1801.06525,
  title  = {K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications},
  author = {Yusuke Kimura},
  journal= {arXiv preprint arXiv:1801.06525},
  year   = {2018}
}