Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Moutard transformation of two-dimensional Dirac operators and
  conformal geometry of surfaces in the four-space   The Moutard transformation for a two-dimensional Dirac operator with a
complex-valued potential is constructed. It is showed that this transformation
relates the potentials of Weierstrass representations of surfaces related by a
composition of the inversion and a reflection with respect to an axis. It is
given an analytical description of an explicit example of such a transformation
which results in a creation of double points on the spectral curve of a Dirac
operator with a double-periodic potential.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph