Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$-Serre duality on singular complex spaces and rational
  singularities   In the present paper, we devise a version of topological $L^2$-Serre duality
for singular complex spaces with arbitrary singularities. This duality is used
to deduce various new $L^2$-vanishing theorems for the
$\bar{\partial}$-equation on singular spaces. It is shown that complex spaces
with rational singularities behave quite tame with respect to the
$\bar{\partial}$-equation in the $L^2$-sense. More precisely: a singular point
is rational if and only if the $L^2$-$\bar{\partial}$-complex is exact in this
point. So, we obtain an $L^2$-$\bar{\partial}$-resolution of the structure
sheaf in rational singular points.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga