Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic inversion of adjunction: L^2 extension theorems with gain   We establish new results on weighted $L^2$ extension of holomorphic top forms
with values in a holomorphic line bundle, from a smooth hypersurface cut out by
a holomorphic function. The weights we use are determined by certain functions
that we call denominators. We give a collection of examples of these
denominators related to the divisor defined by the submanifold.

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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol