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arXiv · 1706.01648

Single point Seshadri constants on rational surfaces

Krishna Hanumanthu·Brian Harbourne
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Abstract

Motivated by a similar result of Dumnicki, K\"uronya, Maclean and Szemberg under a slightly stronger hypothesis, we exhibit irrational single-point Seshadri constants on a rational surface $X$ obtained by blowing up very general points of $\mathbb{P}^2_\mathbb{C}$, assuming only that all prime divisors on $X$ of negative self-intersection are smooth rational curves $C$ with $C^2=-1$. (This assumption is a consequence of the SHGH Conjecture, but it is weaker than assuming the full conjecture.)

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Krishna Hanumanthu, Brian Harbourne. 2017-06-06. Single point Seshadri constants on rational surfaces. https://arxiv.org/abs/1706.01648

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