Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pluripolar hulls and convergence sets   The pluripolar hull of a pluripolar set E in $\mathbb{P}^n$ is the
intersection of all complete pluripolar sets in $\mathbb{P}^n$ that contain
$E$. We prove that the pluripolar hull of each compact pluripolar set in
$\mathbb{P}^n$ is $F_\sigma$. The convergence set of a divergent formal power
series $f(z_{0}, \dots,z_{n})$ is the set of all "directions" $\xi
\in\mathbb{P}^{n}$ along which $f$ is convergent. We prove that the union of
the pluripolar hulls of a countable collection of compact pluripolar sets in
$\mathbb{P}^n$ is the convergence set of some divergent series $f$. The
convergence sets on $\Gamma:=\{[1:z:\psi(z)]: z\in
\mathbb{C}\}\subset\mathbb{C}^2\subset\mathbb{P}^2$, where $\psi$ is a
transcendental entire holomorphic function, are also studied and we obtain that
a subset on $\Gamma$ is a convergence set in $\mathbb{P}^2$ if and only if it
is a countable union of compact projectively convex sets, and hence the union
of a countable collection of convergence sets on $\Gamma$ is a convergence set.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin