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arXiv · 1707.02563

On automorphisms of Enriques surfaces and their entropy

Yuya Matsumoto·Hisanori Ohashi·Sławomir Rams
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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.

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Yuya Matsumoto, Hisanori Ohashi, Sławomir Rams. 2017-12-26. On automorphisms of Enriques surfaces and their entropy. https://doi.org/10.1002/mana.201700329

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