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arXiv · 2407.18678

Rationality of Seshadri constants on blow-ups of ruled surfaces

Krishna Hanumanthu·Cyril J. Jacob·Suhas B. N.·Amit Kumar Singh
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Abstract

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.

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Krishna Hanumanthu, Cyril J. Jacob, Suhas B. N., Amit Kumar Singh. 2024-07-26. Rationality of Seshadri constants on blow-ups of ruled surfaces. https://arxiv.org/abs/2407.18678

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