Extremal hyperelliptic fibrations on rational surfaces

2010/06/24 by Kitagawa, Shinya
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1006.4882

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.

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