Recently Oguiso showed the existence of K3 surfaces that admit a fixed point
free automorphism of positive entropy. The K3 surfaces used by Oguiso have a
particular rank two Picard lattice. We show, using results of Beauville, that
these surfaces are therefore determinantal quartic surfaces. Long ago, Cayley
constructed an automorphism of such determinantal surfaces. We show that
Cayley's automorphism coincides with Oguiso's free automorphism. We also
exhibit an explicit example of a determinantal quartic whose Picard lattice has
exactly rank two and for which we thus have an explicit description of the
automorphism.Comment: 22 pages, 1 figure. We added several improvements, as well as a
figure. A smaller pdf file with the figure in lower resolution (faster on
most viewers) is available by downloading the source under "Other formats
