JournalsrlmVol. 24, No. 2pp. 181–197

Canonical vector heights on K3K3 surfaces – A nonexistence result

  • Shu Kawaguchi

    Kyoto University, Japan
Canonical vector heights on $K3$ surfaces – A nonexistence result cover
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Abstract

A. Baragar introduced a canonical vector height on a K3K3 surface XX defined over a number field, and showed its existence if XX has Picard rank two with infinite automorphism group. In another paper, A. Baragar and R. van Lujik performed numerical computation on certain K3K3 surfaces with Picard rank three, which strongly suggests that, in general, a canonical vector height does not exist. In this note, we prove this last assertion. We compare the set of periodic points of one automorphism with another on certain K3K3 surfaces.

Cite this article

Shu Kawaguchi, Canonical vector heights on K3K3 surfaces – A nonexistence result. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 24 (2013), no. 2, pp. 181–197

DOI 10.4171/RLM/651