The non-degeneracy invariant of Brandhorst and Shimada's families of Enriques surfaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917683954450432 |
|---|---|
| author | Moschetti, Riccardo Rota, Franco Schaffler, Luca |
| author_facet | Moschetti, Riccardo Rota, Franco Schaffler, Luca |
| contents | Brandhorst and Shimada described a large class of Enriques surfaces, called $(τ,\overlineτ)$-generic, for which they gave generators for the automorphism groups and calculated the elliptic fibrations and the smooth rational curves up to automorphisms. In the present paper, we give lower bounds for the non-degeneracy invariant of such Enriques surfaces, we show that in most cases the invariant has generic value $10$, and we present the first known example of complex Enriques surface with infinite automorphism group and non-degeneracy invariant not equal to $10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The non-degeneracy invariant of Brandhorst and Shimada's families of Enriques surfaces Moschetti, Riccardo Rota, Franco Schaffler, Luca Algebraic Geometry 14J28, 14J50, 14Q10 Brandhorst and Shimada described a large class of Enriques surfaces, called $(τ,\overlineτ)$-generic, for which they gave generators for the automorphism groups and calculated the elliptic fibrations and the smooth rational curves up to automorphisms. In the present paper, we give lower bounds for the non-degeneracy invariant of such Enriques surfaces, we show that in most cases the invariant has generic value $10$, and we present the first known example of complex Enriques surface with infinite automorphism group and non-degeneracy invariant not equal to $10$. |
| title | The non-degeneracy invariant of Brandhorst and Shimada's families of Enriques surfaces |
| topic | Algebraic Geometry 14J28, 14J50, 14Q10 |
| url | https://arxiv.org/abs/2309.14981 |