English

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.

Keywords

Cite

@article{arxiv.1006.4882,
  title  = {Extremal hyperelliptic fibrations on rational surfaces},
  author = {Shinya Kitagawa},
  journal= {arXiv preprint arXiv:1006.4882},
  year   = {2010}
}
R2 v1 2026-06-21T15:40:45.311Z