Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morsifications of real plane curve singularities   A real morsification of a real plane curve singularity is a real deformation
given by a family of real analytic functions having only real Morse critical
points with all saddles on the zero level. We prove the existence of real
morsifications for real plane curve singularities having arbitrary real local
branches and pairs of complex conjugate branches satisfying some conditions.
This was known before only in the case of all local branches being real
(A'Campo, Gusein-Zade). We also discuss a relation between real morsifications
and the topology of singularities, extending to arbitrary real morsifications
the Balke-Kaenders theorem, which states that the A'Campo--Gusein-Zade diagram
associated to a morsification uniquely determines the topological type of a
singularity.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat