Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L^2 Castelnuovo-de Franchis, the cup product lemma, and filtered ends of
  Kaehler manifolds   Simple approaches to the proofs of the L^2 Castelnuovo-de Franchis theorem
and the cup product lemma which give new versions are developed. For example,
suppose u and v are two linearly independent closed holomorphic 1-forms on a
bounded geometry connected complete Kaehler manifold X with v in L^2. According
to a version of the L^2 Castelnuovo-de Franchis theorem obtained in this paper,
if u and v are pointwise linearly dependent, then there exists a surjective
proper holomorphic mapping of X onto a Riemann surface for which u and v are
pull-backs. Previous versions required both forms to be in L^2.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg