Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Role of the Gradient Term of the Bochner-Kodaira Formula in Coherent
  Sheaf Extension   In applying the Bochner-Kodaira formula with boundary term to solve the
$\bar\partial$ equation with $L^2$ estimates, the gradient term is usually not
used. In this note we use the gradient term to construct holomorphic sections
to prove the Thullen-type extension across codimension $1$ for holomorphic
vector bundles with Hermitian metric whose curvature is $L^p$ for some $p>1$.

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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
1
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: acc-phys
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics