Extremal hyperelliptic fibrations on rational surfaces
Algebraic Geometry
2010-06-28 v1
Abstract
We consider a rational surface with a relatively minimal fibration. Picard number of a such fibred surface is bounded in terms of the genus of a general fibre. When Picard number is the maximum for any given genus, we characterize a such fibred surface whose Mordell-Weil group is trivial by singular fibres. Furthermore, we describe the defining equation explicitly.
Cite
@article{arxiv.1006.4882,
title = {Extremal hyperelliptic fibrations on rational surfaces},
author = {Shinya Kitagawa},
journal= {arXiv preprint arXiv:1006.4882},
year = {2010}
}