Comptes Rendus
no. 9-10
Algebraic Geometry
Families of curves over P1 with 3 singular fibers
[Familles de courbes sur P1 avec trois fibres singulières]

Présenté par : Claire Voisin

Cheng Gong1 ; Xin Lu1 ; Sheng-Li Tan1
1 Department of Mathematics, East China Normal University, Dongchuan RD 500, Shanghai 200421, PR China
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 375-380.

Soit f:S→P1 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 2g⩽−KS2⩽4g−4. Nous construisons également des exemples montrant quʼil existe de telles fibrations pour une infinité de g.

Suppose f:S→P1 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 2g⩽−KS2⩽4g−4. We construct some examples to show that such fibrations exist for infinitely many g.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.05.002
Cheng Gong 1 ; Xin Lu 1 ; Sheng-Li Tan 1

1 Department of Mathematics, East China Normal University, Dongchuan RD 500, Shanghai 200421, PR China 
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Cheng Gong; Xin Lu; Sheng-Li Tan. 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. https://comptes-rendus.academie-sciences.fr/mathematique/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.

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