Pencils of genus two curves on rational surfaces
Algebraic Geometry
2010-06-24 v1
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.
Keywords
Cite
@article{arxiv.1006.4372,
title = {Pencils of genus two curves on rational surfaces},
author = {Shinya Kitagawa},
journal= {arXiv preprint arXiv:1006.4372},
year = {2010}
}