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The Szpiro inequality for higher genus fibrations

Arnaud Beauville
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Abstract

Let f : S --> B be a non-trivial family of semi-stable curves of genus g, N the number of critical points of f and s the number of singular fibres. We prove the inequality N < (4g+2)(s+2g(B)-2) .

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Arnaud Beauville. 2001-09-13. The Szpiro inequality for higher genus fibrations. https://arxiv.org/abs/math/0109080

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