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Izvestiya: Mathematics, 2013, Volume 77, Issue 3, Pages 571–580
DOI: https://doi.org/10.1070/IM2013v077n03ABEH002649
(Mi im8017)
 

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
References:
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.
Funding agency Grant number
Japan Society for the Promotion of Science (C) 20540051
Received: 26.06.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 3, Pages 139–148
DOI: https://doi.org/10.4213/im8017
Bibliographic databases:
Document Type: Article
UDC: 512.7
MSC: 14J27, 14J28, 14H40
Language: English
Original paper language: English
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
Citation in format AMSBIB
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\paper Elliptic fibrations of maximal rank on a~supersingular K3 surface
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\issue 3
\pages 139--148
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\jour Izv. Math.
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  • https://www.mathnet.ru/eng/im8017
  • https://doi.org/10.1070/IM2013v077n03ABEH002649
  • https://www.mathnet.ru/eng/im/v77/i3/p139
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:447
    Russian version PDF:190
    English version PDF:5
    References:62
    First page:16
     
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