A Note on a Conjecture of Xiao

Details A Note on a Conjecture of Xiao A Note on a Conjecture of Xiao

1999-01-27

arxiv.org/abs/math/9901128v1

Mathematics

Algebraic Geometry

2 pages; Latex

Scientific paper

Let f:S ->B be a relatively minimal fibred surface. In this note we give a
partial affirmative answer to a conjecture of Xiao, proving that the direct
image of the relative dualizing sheaf of $f$ is ample when the slope of the
fibration is less than 4, if the general fibre of $f$ is non-hyperelliptic or
the genus of the fibre or of the base curve is low.

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