Suppose 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 . We construct some examples to show that such fibrations exist for infinitely many g.
Soit 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 . Nous construisons également des exemples montrant quʼil existe de telles fibrations pour une infinité de g.
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Cheng Gong 1; Xin Lu 1; Sheng-Li Tan 1
@article{CRMATH_2013__351_9-10_375_0, author = {Cheng Gong and Xin Lu and Sheng-Li Tan}, title = {Families of curves over $ {\mathbb{P}}^{1}$ with 3 singular fibers}, journal = {Comptes Rendus. Math\'ematique}, pages = {375--380}, publisher = {Elsevier}, volume = {351}, number = {9-10}, year = {2013}, doi = {10.1016/j.crma.2013.05.002}, language = {en}, }
TY - JOUR AU - Cheng Gong AU - Xin Lu AU - Sheng-Li Tan TI - Families of curves over $ {\mathbb{P}}^{1}$ with 3 singular fibers JO - Comptes Rendus. Mathématique PY - 2013 SP - 375 EP - 380 VL - 351 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2013.05.002 LA - en ID - CRMATH_2013__351_9-10_375_0 ER -
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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