The Enriques surface of minimal entropy

2025/11/26 by Martin, Gebhard, Mezzedimi, Giacomo, Veniani, Davide Cesare
#14J28 #14J50 #37P25 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.21286

Abstract

Lehmer's number λ₁₀ is the smallest dynamical degree greater than 1 that can occur for an automorphism of an algebraic surface. We show that λ₁₀ cannot be realized by automorphisms of Enriques surfaces in odd characteristic, extending a result of Oguiso over the complex numbers. In contrast, we prove that in characteristic 2 there exists a unique Enriques surface that admits an automorphism with dynamical degree λ₁₀. We also provide explicit equations for the surface as well as for all conjugacy classes of automorphisms that realize λ₁₀.

Citations

• Automorphism group schemes of bielliptic and quasi-bielliptic surfaces
• Enriques surfaces with normal K3-like coverings
• The representations of the automorphism groups and the Frobenius invariants of K3 surfaces
• Moduli and periods of simply connected Enriques surfaces
• Algebraic versus topological entropy for surfaces over finite fields
• The third smallest Salem number in automorphisms of K3 surfaces

Related

• Salem numbers and Enriques surfaces
• An explicit Enriques surface with an automorphism of minimum entropy
• Enriques surfaces of zero entropy
• The third smallest Salem number in automorphisms of K3 surfaces
• Automorphisms of unnodal Enriques surfaces