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

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

1994-11-08

arxiv.org/abs/alg-geom/9411002v1

Mathematics

Algebraic Geometry

6 pages, AmSTeX

Scientific paper

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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