Pencils of genus two curves on rational surfaces

Abstract

We consider relatively minimal fibrations of curves of genus two on rational surfaces whose Picard numbers are not maximal. By birational morphisms, such fibred surfaces are interpreted as pencils of plane curves. We show that only four are canonical, among a variety of possible models. For each canonical pencil, we give an example with trivial Mordell-Weil group.

References in corpus (1)

• Extremal hyperelliptic fibrations on rational surfaces

Cited by in corpus (2)

• Extremal hyperelliptic fibrations on rational surfaces
• Arithmetic rank bounds for abelian varieties over function fields