The minimal number of singular fibers of a semistable curves over P1
Abstract
In this paper, we shall prove Beauville's conjecture: if f:S P1 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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