Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Yau's characterization of isolated homogeneous hypersurface
  singularities   Using the semicontinuity of the Milnor number and the {\L}ojasiewicz
exponent, we give a simple proof of Yau's characterization of isolated
homogenous hypersurface singularities.

8
The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ