Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On structures of normal forms of complex points of small
  $\mathcal{C}^{2}$-perturbations of real $4$-manifolds embedded in a complex
  $3$-manifold   We extend our previous result on the behavior of the quadratic part of a
complex points of a small $\mathcal{C}^{2}$-perturbation of a real $4$-manifold
embedded in a complex $3$-manifold. We describe the change of the structure of
a normal form of a complex point. It is an immediate consequence of a theorem
clarifying how small perturbations can change the bundle of a pair of one
arbitrary and one symmetric $2\times 2$ matrix with respect to an action of a
certain linear group.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg