Remarks on the positivity of the cotangent bundle of an Enriques surface
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915831361830912 |
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| author | Faro, Dario |
| author_facet | Faro, Dario |
| contents | Let $S$ be an Enriques surface. In this paper we study the semistability of the restriction $Ω_{S}|_C$ for a general curve $C \in |H|$, where $H$ is a globally generated and ample line bundle on $S$. We show that $Ω_{S}|_C$ is semistable when $H^2 \ge 6$, or when $H^2 \ge 2$ and $S$ is very general. Moreover, we give explicit constructions of families of smooth irreducible curves that destabilize $Ω_S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on the positivity of the cotangent bundle of an Enriques surface Faro, Dario Algebraic Geometry Let $S$ be an Enriques surface. In this paper we study the semistability of the restriction $Ω_{S}|_C$ for a general curve $C \in |H|$, where $H$ is a globally generated and ample line bundle on $S$. We show that $Ω_{S}|_C$ is semistable when $H^2 \ge 6$, or when $H^2 \ge 2$ and $S$ is very general. Moreover, we give explicit constructions of families of smooth irreducible curves that destabilize $Ω_S$. |
| title | Remarks on the positivity of the cotangent bundle of an Enriques surface |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.02965 |