Canonical vector heights on $K3$ surfaces – A nonexistence result

Shu Kawaguchi
2013 Rendiconti Lincei - Matematica e Applicazioni  
A. Baragar introduced a canonical vector height on a K3 surface X defined over a number field, and showed its existence if X has Picard rank two with infinite automorphism group. In another paper, A. Baragar and R. van Lujik performed numerical computation on certain K3 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
more » ... omorphism with another on certain K3 surfaces.
doi:10.4171/rlm/651 fatcat:zmd54qy6r5d2dgl4lyfwlcyhea