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Elliptic surfaces of
Kodaira dimension zero
Kentaro Mitsui |
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Vol. 318 (2022), No. 2, 249–273
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Abstract |
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We classify elliptic surfaces of Kodaira dimension zero by completing the Bombieri–Mumford list of possible configurations of invariants, which was obtained by means of the canonical bundle formula and other restrictions. In the characteristic zero case, an example of each configuration can be constructed by means of logarithmic transformation and algebraization. In the positive characteristic case, we show that some configurations do not appear, and we determine which configurations actually appear. |
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Keywords
elliptic surfaces, classification, positive characteristic,
arithmetic curves
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Mathematical Subject Classification
Primary: 11G07, 14G17, 14J10, 14J27
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Milestones
Received: 1 October 2021
Revised: 6 March 2022
Accepted: 17 March 2022
Published: 20 August 2022
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Authors |
| Kentaro Mitsui | |
| Department of Mathematics Graduate School of Science Kobe University Hyogo Japan |
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