On automorphisms of Enriques surfaces and their entropy

Yuya Matsumoto, Hisanori Ohashi and Sławomir Rams

Mathematische Nachrichten, 2018, vol. 291, issue 13, 2084-2098

Abstract: 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 lower 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.

Date: 2018
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https://doi.org/10.1002/mana.201700329

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