Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-circled singularities, Lelong numbers, and integrability index   By comparing Green functions of multi-circled plurisubharmonic singularities
in the n-domensional complex space to their indicators, we obtain formulas for
the higher Lelong numbers and integrability index for such singularities and
extend Howald's result on multiplier ideals for monomial ideals to
multi-circled singularities. This also leads to an elementary proof of the
relations between the k-th Lelong numbers and the integrability index. For k=1
and arbitrary plurisubharmonic functions the inequality is due to Skoda, and
for k=n and any plurisubharmonic function with isolated singularity the
relation is due to Demailly. We also describe multi-circled functions for which
the inequalities are equalities. By a reduction to Demailly's inequality we
prove these inequalities in the general case of plurisubharmonic functions as
well. In addition, we get a description of all plurisubharmonic singularities
whose integrability index is given by the lower bound in Skoda's inequality.

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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an