Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equimultiplicity of families of map germs from $\mathbb{C}^2$ to
  $\mathbb{C}^3$   In 1971, Zariski proposed some questions in Theory of Singularities. One of
such problems is the so-called, nowadays, Zariski's multiplicity conjecture. In
this work, we consider the version of this conjecture for families. We answer
positively Zariski's multiplicity conjecture for a special class of
non-isolated singularities.

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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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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: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol