Rationality of Seshadri constants on blow-ups of ruled surfaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909269625929728 |
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| author | Hanumanthu, Krishna Jacob, Cyril J. N., Suhas B. Singh, Amit Kumar |
| author_facet | Hanumanthu, Krishna Jacob, Cyril J. N., Suhas B. Singh, Amit Kumar |
| contents | In this note, we continue the study of Seshadri constants on blow-ups of Hirzebruch surfaces initiated in arXiv:2312.14555. Now we consider blow-ups of ruled surfaces more generally. We propose a conjecture for classifying all the negative self-intersection curves on the blow-up of a ruled surface at very general points, analogous to the $(-1)$-curves conjecture in $\mathbb{P}^2$. Assuming this conjecture is true, we exhibit an ample line bundle with an irrational Seshadri constant at a very general point on such a surface. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_18678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rationality of Seshadri constants on blow-ups of ruled surfaces Hanumanthu, Krishna Jacob, Cyril J. N., Suhas B. Singh, Amit Kumar Algebraic Geometry 14C20, 14E05, 14J26 In this note, we continue the study of Seshadri constants on blow-ups of Hirzebruch surfaces initiated in arXiv:2312.14555. Now we consider blow-ups of ruled surfaces more generally. We propose a conjecture for classifying all the negative self-intersection curves on the blow-up of a ruled surface at very general points, analogous to the $(-1)$-curves conjecture in $\mathbb{P}^2$. Assuming this conjecture is true, we exhibit an ample line bundle with an irrational Seshadri constant at a very general point on such a surface. |
| title | Rationality of Seshadri constants on blow-ups of ruled surfaces |
| topic | Algebraic Geometry 14C20, 14E05, 14J26 |
| url | https://arxiv.org/abs/2407.18678 |