Rationality of Seshadri constants on blow-ups of ruled surfaces
| Autor: | Hanumanthu, Krishna, Jacob, Cyril J., N., Suhas B., Singh, Amit Kumar |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 13 Pages |
| Databáze: | arXiv |
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