Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.05630 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917200546234368 |
|---|---|
| author | Nollet, Scott Rao, A. P. |
| author_facet | Nollet, Scott Rao, A. P. |
| contents | If $\mathcal E, \mathcal F$ are vector bundles of ranks $r-1,r$ on a smooth fourfold $X$ and $\mathcal{Hom}(\mathcal E,\mathcal F)$ is globally generated, it is well known that the general map $ϕ: \mathcal E \to \mathcal F$ is injective and drops rank along a smooth surface. Chang improved on this with a filtered Bertini theorem. We strengthen these results by proving variants in which (a) $\mathcal F$ is not a vector bundle and (b) $\mathcal{Hom}(\mathcal E,\mathcal F)$ is not globally generated. As an application, we give examples of even linkage classes of surfaces on $\mathbb P^4$ in which all integral surfaces are smoothable, including the linkage classes associated with the Horrocks-Mumford surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoothing surfaces on fourfolds Nollet, Scott Rao, A. P. Algebraic Geometry 14F06, 14J35, 14M07, 14M06 If $\mathcal E, \mathcal F$ are vector bundles of ranks $r-1,r$ on a smooth fourfold $X$ and $\mathcal{Hom}(\mathcal E,\mathcal F)$ is globally generated, it is well known that the general map $ϕ: \mathcal E \to \mathcal F$ is injective and drops rank along a smooth surface. Chang improved on this with a filtered Bertini theorem. We strengthen these results by proving variants in which (a) $\mathcal F$ is not a vector bundle and (b) $\mathcal{Hom}(\mathcal E,\mathcal F)$ is not globally generated. As an application, we give examples of even linkage classes of surfaces on $\mathbb P^4$ in which all integral surfaces are smoothable, including the linkage classes associated with the Horrocks-Mumford surface. |
| title | Smoothing surfaces on fourfolds |
| topic | Algebraic Geometry 14F06, 14J35, 14M07, 14M06 |
| url | https://arxiv.org/abs/2501.05630 |