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The minimal number of singular fibers of a semistable curves over P^1

Sheng-Li Tan
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Abstract

In this paper, we shall prove Beauville's conjecture: if $f:S \to P^1$ is a non-trivial semistable fibration of genus g>1, then $f$ admits at least 5 singular fibers. We have also constructed an example of genus 2 with 5 singular fibers. This paper will appear in the Journal of Algebraic Geometry.

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Sheng-Li Tan. 1994-11-08. The minimal number of singular fibers of a semistable curves over P^1. https://arxiv.org/abs/alg-geom/9411002

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