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A Note on a Conjecture of Xiao

Miguel A. Barja·Francesco Zucconi
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Abstract

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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Miguel A. Barja, Francesco Zucconi. 1999-01-27. A Note on a Conjecture of Xiao. https://arxiv.org/abs/math/9901128

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