Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Seshadri constants and special configurations of points in the
  projective plane   In the present note, we focus on certain properties of special curves that
might be used in the theory of multi-point Seshadri constants for ample line
bundles on the complex projective plane. In particular, we provide three
Ein-Lazarsfeld-Xu-type lemmas for plane curves and a lower bound on the
multi-point Seshadri constant of $\mathcal{O}_{\mathbb{P}^{2}}(1)$ under the
assumption that the chosen points are not very general. In the second part, we
focus on certain arrangements of points in the plane which are given by line
arrangements. We show that in some cases the multi-point Seshadri constants of
$\mathcal{O}_{\mathbb{P}^{2}}(1)$ centered at singular loci of line
arrangements are computed by lines from the arrangement having some extremal
properties.

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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas