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We will work over the complex numbers C.

there exist a fibration of genus two over P^1 with only 3 singular fibres but one is semi-stable fiber.

there not exist a fibration of genus two over P^1 with only 3 singular fibres but three are all semi-stable fibers.

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Related question: mathoverflow.net/questions/64112/… –  Francesco Polizzi May 22 '11 at 15:39
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See this paper: arxiv.org/pdf/alg-geom/9411002. –  J.C. Ottem May 22 '11 at 22:38

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