Algebraic Geometry
Families of curves over P1 with 3 singular fibers
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 375-380.

Suppose f:SP1 is a fibration of genus g with 3 singular fibers and two of them are semistable. We show that the Mordell–Weil group of f is finite, the surface S is rational and 2gKS24g4. We construct some examples to show that such fibrations exist for infinitely many g.

Soit f:SP1 une fibration de genre g avec trois fibres singulières, dont deux dʼentre elles sont semi-stables. Nous montrons que le groupe de Mordell–Weil de f est fini, que la surface S est rationnelle et que 2gKS24g4. Nous construisons également des exemples montrant quʼil existe de telles fibrations pour une infinité de g.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.05.002
Gong, Cheng 1; Lu, Xin 1; Tan, Sheng-Li 1

1 Department of Mathematics, East China Normal University, Dongchuan RD 500, Shanghai 200421, PR China
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Gong, Cheng; Lu, Xin; Tan, Sheng-Li. Families of curves over $ {\mathbb{P}}^{1}$ with 3 singular fibers. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 375-380. doi : 10.1016/j.crma.2013.05.002. http://www.numdam.org/articles/10.1016/j.crma.2013.05.002/

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This work is supported by NSFC. The second author is partially supported by ECNU Reward for Excellent Doctors in Academics.