Enriques surfaces with non-generic non-degeneracy
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915689906831360 |
|---|---|
| author | Moschetti, Riccardo Rota, Franco Schaffler, Luca |
| author_facet | Moschetti, Riccardo Rota, Franco Schaffler, Luca |
| contents | We study the non-degeneracy invariant $\mathrm{nd}(Y)$ of complex Enriques surfaces in families. Our first main result shows that $\mathrm{nd}(Y)$ cannot increase under specialization. The second main result is the conclusion of the computation of the non-degeneracy invariant for the $155$ families of $(τ,\overlineτ)$-generic surfaces introduced by Brandhorst and Shimada. Of the previously known $144$ cases, only $3$ satisfy $\mathrm{nd}(Y)\neq10$, which is the non-degeneracy invariant of a general Enriques surface. The remaining $11$ families studied in this article also have non-generic non-degeneracy. To compute this, we produce upper bounds on $\mathrm{nd}(Y)$ by refining this invariant into two others: the Fano and Mukai non-degeneracy invariants, which are related to two different classes of projective realizations of Enriques surfaces. As a result, we find the first known examples of Enriques surfaces with $\mathrm{nd}(Y)=9$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enriques surfaces with non-generic non-degeneracy Moschetti, Riccardo Rota, Franco Schaffler, Luca Algebraic Geometry 14J28, 14J50, 14Q10 We study the non-degeneracy invariant $\mathrm{nd}(Y)$ of complex Enriques surfaces in families. Our first main result shows that $\mathrm{nd}(Y)$ cannot increase under specialization. The second main result is the conclusion of the computation of the non-degeneracy invariant for the $155$ families of $(τ,\overlineτ)$-generic surfaces introduced by Brandhorst and Shimada. Of the previously known $144$ cases, only $3$ satisfy $\mathrm{nd}(Y)\neq10$, which is the non-degeneracy invariant of a general Enriques surface. The remaining $11$ families studied in this article also have non-generic non-degeneracy. To compute this, we produce upper bounds on $\mathrm{nd}(Y)$ by refining this invariant into two others: the Fano and Mukai non-degeneracy invariants, which are related to two different classes of projective realizations of Enriques surfaces. As a result, we find the first known examples of Enriques surfaces with $\mathrm{nd}(Y)=9$. |
| title | Enriques surfaces with non-generic non-degeneracy |
| topic | Algebraic Geometry 14J28, 14J50, 14Q10 |
| url | https://arxiv.org/abs/2512.18812 |