On the geometry of Halphen surfaces, associated K3 surfaces, and F-theory

Research paper by Yusuke Kimura

Indexed on: 19 Jan '18Published on: 19 Jan '18Published in: arXiv - High Energy Physics - Theory


We study the structures of a family of rational elliptic surfaces, called Halphen surfaces of index 2. These surfaces have bisections, but they do not have a global section. We construct several examples of Halphen surfaces of index 2 with type $I_{n}$ fibers. By considering double covers of the Halphen surfaces of index 2, we obtain genus-one fibered K3 surfaces without a global section. Consequently, we obtain examples of K3 surfaces without a section with type $I_n$ fibers. Furthermore, we consider F-theory compactifications on the resulting K3 surfaces without a section times a K3 surface. We find that SU(5) gauge symmetry arises in one of these compactifications.