The Cayley-Oguiso automorphism of positive entropy on a K3 surface
Abstract
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.
Keywords
Cite
@article{arxiv.1208.1016,
title = {The Cayley-Oguiso automorphism of positive entropy on a K3 surface},
author = {Dino Festi and Alice Garbagnati and Bert van Geemen and Ronald van Luijk},
journal= {arXiv preprint arXiv:1208.1016},
year = {2012}
}
Comments
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"