Vol. 318, No. 2, 2022

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Elliptic surfaces of Kodaira dimension zero

Kentaro Mitsui

Vol. 318 (2022), No. 2, 249–273

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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elliptic surfaces, classification, positive characteristic, arithmetic curves
Mathematical Subject Classification
Primary: 11G07, 14G17, 14J10, 14J27
Received: 1 October 2021
Revised: 6 March 2022
Accepted: 17 March 2022
Published: 20 August 2022
Kentaro Mitsui
Department of Mathematics
Graduate School of Science
Kobe University