Journal of the Mathematical Society of Japan

Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree

Xun YU

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We study the maximal Salem degree of automorphisms of K3 surfaces via elliptic fibrations. In particular, we establish a characterization of such maximum in terms of elliptic fibrations with infinite automorphism groups. As an application, we show that any supersingular K3 surface in odd characteristic has an automorphism the entropy of which is the natural logarithm of a Salem number of degree 22.

Article information

J. Math. Soc. Japan, Volume 70, Number 3 (2018), 1151-1163.

Received: 24 August 2016
Revised: 20 January 2017
First available in Project Euclid: 25 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J28: $K3$ surfaces and Enriques surfaces 14J50: Automorphisms of surfaces and higher-dimensional varieties
Secondary: 14D06: Fibrations, degenerations 14G99: None of the above, but in this section

K3 surfaces automorphisms elliptic fibrations Salem numbers


YU, Xun. Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree. J. Math. Soc. Japan 70 (2018), no. 3, 1151--1163. doi:10.2969/jmsj/75907590.

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