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Miranda–Persson’s
problem on extremal elliptic K3 surfaces
Enrique Artal Bartolo, Hiro-o Tokunaga and De-Qi Zhang |
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Vol. 202 (2002), No. 1, 37–72
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Abstract |
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In one of their early works, Miranda and Persson have classified all possible configurations of singular fibers for semistable extremal elliptic fibrations on K3 surfaces. They also obtained the Mordell-Weil groups in terms of the singular fibers except for 17 cases where the determination and the uniqueness of the groups were not settled. In this paper, we settle these problems completely. We also show that for all cases with ‘larger’ Mordell-Weil groups, this group, together with the singular fibre type, determines uniquely the fibration structure of the K3 surface (up to based fibre-space isomorphisms). |
Milestones
Received: 15 February 2000
Published: 1 January 2002
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Authors |
| Enrique Artal Bartolo | |
| Departamento de Matemáticas Universidad de Zaragoza Campus Plaza San Francisco s/n E-50009 Zaragoza, Spain |
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| Hiro-o Tokunaga | |
| Department of Mathematics Kochi University Kochi 780, Japan |
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| De-Qi Zhang | |
| Department of Mathematics National University of Singapore Lower Kent Ridge Road Singapore 119260 |
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