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This article is cited in 2 scientific papers (total in 2 papers)
Elliptic fibrations of maximal rank on a supersingular K3 surface
T. Shioda Rikkyo University, Department of Mathematics, Tokyo, Japan
Abstract:
We study a class of elliptic $\mathrm{K3}$ surfaces defined by an explicit Weierstrass equation to find elliptic fibrations of maximal rank on $\mathrm{K3}$ surface in positive characteristic. In particular, we show that the supersingular $\mathrm{K3}$ surface of Artin invariant 1 (unique by Ogus) admits at least one elliptic fibration with maximal rank 20 in every characteristic $p>7$, $p\ne 13$, and further that the number, say $N(p)$, of such elliptic fibrations (up to isomorphisms), is unbounded as $p\to\infty$; in fact, we prove that $\lim_{p\to\infty} N(p)/p^{2} \geqslant (1/12)^{2}$.
Bibliography: 19 titles.
Keywords:
$\mathrm{K3}$ surface, Mordell–Weil lattice, Artin invariant.
Received: 26.06.2012
Citation:
T. Shioda, “Elliptic fibrations of maximal rank on a supersingular K3 surface”, Izv. RAN. Ser. Mat., 77:3 (2013), 139–148; Izv. Math., 77:3 (2013), 571–580
Linking options:
https://www.mathnet.ru/eng/im8017https://doi.org/10.1070/IM2013v077n03ABEH002649 https://www.mathnet.ru/eng/im/v77/i3/p139
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Abstract page: | 447 | Russian version PDF: | 190 | English version PDF: | 5 | References: | 62 | First page: | 16 |
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