Extremal hyperelliptic fibrations on rational surfaces

Details Extremal hyperelliptic fibrations on rational surfaces Extremal hyperelliptic fibrations on rational surfaces

2010-06-24

arxiv.org/abs/1006.4882v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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