On automorphisms of Enriques surfaces and their entropy
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 may be the minimal dynamical degree on Enriques surfaces and for which the existence of geometric automorphisms is unknown.
Keywords
Cite
@article{arxiv.1707.02563,
title = {On automorphisms of Enriques surfaces and their entropy},
author = {Yuya Matsumoto and Hisanori Ohashi and Sławomir Rams},
journal= {arXiv preprint arXiv:1707.02563},
year = {2018}
}
Comments
16 pages / v2: some refinements on the theorems and the proofs, and also attached plain text lists of Salem numbers related to the problem