Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Very general monomial valuations of $\mathbb{P}^2$ and a Nagata type
  conjecture   It is well known that multi-point Seshadri constants for a small number $s$
of points in the projective plane are submaximal. It is predicted by the Nagata
conjecture that their values are maximal for $s\geq 9$ points. Tackling the
problem in the language of valuations one can make sense of $s$ points for any
positive real $s\geq 1$. We show somewhat surprisingly that a Nagata-type
conjecture should be valid for $s\geq 8+1/36$ points and we compute explicitly
all Seshadri constants (expressed here as the asymptotic maximal vanishing
element) for $s\leq 7+1/9$.

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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph