The Enriques surface of minimal entropy
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912730557972480 |
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| author | Martin, Gebhard Mezzedimi, Giacomo Veniani, Davide Cesare |
| author_facet | Martin, Gebhard Mezzedimi, Giacomo Veniani, Davide Cesare |
| contents | Lehmer's number $λ_{10}$ is the smallest dynamical degree greater than $1$ that can occur for an automorphism of an algebraic surface. We show that $λ_{10}$ 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 $λ_{10}$. We also provide explicit equations for the surface as well as for all conjugacy classes of automorphisms that realize $λ_{10}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Enriques surface of minimal entropy Martin, Gebhard Mezzedimi, Giacomo Veniani, Davide Cesare Algebraic Geometry Dynamical Systems 14J28, 14J50, 37P25 Lehmer's number $λ_{10}$ is the smallest dynamical degree greater than $1$ that can occur for an automorphism of an algebraic surface. We show that $λ_{10}$ 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 $λ_{10}$. We also provide explicit equations for the surface as well as for all conjugacy classes of automorphisms that realize $λ_{10}$. |
| title | The Enriques surface of minimal entropy |
| topic | Algebraic Geometry Dynamical Systems 14J28, 14J50, 37P25 |
| url | https://arxiv.org/abs/2511.21286 |