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arXiv · 1903.01729

Bounded negativity and Harbourne constants on ruled surfaces

Krishna Hanumanthu·Aditya Subramaniam
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Abstract

Let $X$ be a smooth projective surface and let $\mathcal{C}$ be an arrangement of curves on $X$. The Harbourne constant of $\mathcal{C}$ was defined as a way to investigate the occurrence of curves of negative self-intersection on blow ups of $X$. This is related to the bounded negativity conjecture which predicts that the self-intersection number of all reduced curves on a surface is bounded below by a constant. We consider a geometrically ruled surface $X$ over a smooth curve and give lower bounds for the Harbourne constants of transversal arrangements of curves on $X$.

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Krishna Hanumanthu, Aditya Subramaniam. 2019-03-05. Bounded negativity and Harbourne constants on ruled surfaces. https://arxiv.org/abs/1903.01729

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