Automorphisms of K3 surfaces, signatures, and isometries of lattices

Abstract

Every Salem numbers of degree 4,6,8,12,14 or 16 is the dynamical degree of an automorphism of a non-projective K3 surface. We define a notion of signature of an automorphism, and use it to give a necessary and sufficient condition for Salem numbers of degree 10 and 18 to be realized as the dynamical degree of such an automorphism. The first part of the paper contains results on isometries of lattices.Comment: This paper contains several (but not all) of the results of arXiv:2107.07583, as well as new results. arXiv admin note: text overlap with arXiv:2107.07583. Changes in version 2 : added reference to Takada's result on degree 20 Salem numbers, changes (mainly) in Sections 7 and 15. Changes in version 3 : added two sections on automorphisms of projective K3 surfaces (sections 26 and 27