The automorphism group of an Apéry-Fermi K3 surface
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908348630171648 |
|---|---|
| author | Shimada, Ichiro |
| author_facet | Shimada, Ichiro |
| contents | An Apéry-Fermi K3 surface is a complex K3 surface of Picard number 19 that is birational to a general member of a certain one-dimensional family of affine surfaces related to the Fermi surface in solid-state physics. This K3 surface is also linked to a recurrence relation that appears in the famous proof of the irrationality of zeta(3) by Apéry. We compute the automorphism group Aut(X) of the Apéry-Fermi K3 surface X using Borcherds' method. We describe Aut(X) in terms of generators and relations. Moreover, we determine the action of Aut(X) on the set of ADE-configurations of smooth rational curves on X for some ADE-types. In particular, we show that Aut(X) acts transitively on the set of smooth rational curves, and that it partitions the set of pairs of disjoint smooth rational curves into two orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The automorphism group of an Apéry-Fermi K3 surface Shimada, Ichiro Algebraic Geometry An Apéry-Fermi K3 surface is a complex K3 surface of Picard number 19 that is birational to a general member of a certain one-dimensional family of affine surfaces related to the Fermi surface in solid-state physics. This K3 surface is also linked to a recurrence relation that appears in the famous proof of the irrationality of zeta(3) by Apéry. We compute the automorphism group Aut(X) of the Apéry-Fermi K3 surface X using Borcherds' method. We describe Aut(X) in terms of generators and relations. Moreover, we determine the action of Aut(X) on the set of ADE-configurations of smooth rational curves on X for some ADE-types. In particular, we show that Aut(X) acts transitively on the set of smooth rational curves, and that it partitions the set of pairs of disjoint smooth rational curves into two orbits. |
| title | The automorphism group of an Apéry-Fermi K3 surface |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.11025 |