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arXiv · 1507.06391

Positivity of line bundles on general blow ups of $\mathbb{P}^2$

Krishna Hanumanthu
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Abstract

Let $X$ be the blow up of $\mathbb{P}^2$ at $r$ general points $p_1,\ldots,p_r \in \mathbb{P}^2$. We study line bundles on $X$ given by plane curves of degree $d$ passing through $p_i$ with multiplicity $m_i$. We establish conditions for ampleness, very ampleness and global generation of such line bundles.

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Krishna Hanumanthu. 2015-07-23. Positivity of line bundles on general blow ups of $\mathbb{P}^2$. https://arxiv.org/abs/1507.06391

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