Linear systems on rational surfaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911407137619968 |
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| author | Jacob, Cyril J. Sebastian, Ronnie |
| author_facet | Jacob, Cyril J. Sebastian, Ronnie |
| contents | Motivated by various equivalent versions of the SHGH conjecture for $\mathbb{P}^2$ blown up at very general points, we propose a similar conjecture for Hirzebruch surfaces. We prove that this conjecture is true for the Hirzebruch surface $\mathbb{F}_e$ blown up at $r\leqslant e+4$ very general points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21958 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear systems on rational surfaces Jacob, Cyril J. Sebastian, Ronnie Algebraic Geometry 14C20, 14J26, 14E05 Motivated by various equivalent versions of the SHGH conjecture for $\mathbb{P}^2$ blown up at very general points, we propose a similar conjecture for Hirzebruch surfaces. We prove that this conjecture is true for the Hirzebruch surface $\mathbb{F}_e$ blown up at $r\leqslant e+4$ very general points. |
| title | Linear systems on rational surfaces |
| topic | Algebraic Geometry 14C20, 14J26, 14E05 |
| url | https://arxiv.org/abs/2601.21958 |