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

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.

6 pages, AmSTeX

References in corpus (1)

• Height inequality of algebraic points on curves over functional fields

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