On automorphisms of Enriques surfaces and their entropy

Yuya Matsumoto, Hisanori Ohashi, Sławomir Rams

Published 2017-07-09Version 1

Consider an arbitrary automorphism of an Enriques surface with its lift to the covering K3 surface. We prove a bound of the order of the lift acting on the anti-invariant cohomology sublattice of the Enriques involution. We use it to obtain some mod 2 constraint on the original automorphism. As an application, we give a necessary condition for Salem numbers to be dynamical degrees on Enriques surfaces and obtain a new bound on the minimal value. In the Appendix, we give a complete list of Salem numbers that potentially could be the minimal dynamical degree on Enriques surfaces and for which the existence of geometric automorphisms is unknown.