On the stable dynamical spectrum of complex surfaces

Abstract

We characterize Salem numbers which have some power arising as dynamical degree of an automorphism on a complex (projective) 2-Torus, K3 or Enriques surface. 10 points, or a blow up of a 2-Torus, a K3 or an Enriques surface [8]. Let K be a class of surfaces. We define the dynamical spectrum of surfaces of type K as Λ(K, C) = {λ(F )|F ∈ Bir(X), X/C is a K surface}, and its counterpart for projective surfacesIf X is a surface of type K ∈ { 2-Torus, K3, Enriques }, then its canonical divisor is nef and hence Bir(X) = Aut(X). The Kummer construction and the fact that the universal cover of an Enriques surface is a K3 surface give the inclusions Λ(2-Tori, C), Λ(Enriques, C) ⊆ Λ(K3, C).

Salem numbers of automorphisms of K3 surfaces with Picard number 4

“…For minimal Salem numbers of automorphisms of K3 surfaces, we refer to [7,8]. Moreover, for similar results on complex tori, Enriques surfaces and K3 surfaces, we refer to [1,2,12,13,16].…”