Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The complex separation and extensions of Rokhlin congruence for curves
  on surfaces   The subject of this paper is the problem of arrangement of real algebraic
curves on real algebraic surfaces. In this paper we extend Rokhlin,
Kharlamov-Gudkov-Krakhnov and Kharlamov-Marin congruences for curves on
surfaces and give some applications of this extension.
  For some pairs consisting of a surface and a curve on this surface (in
particular for M-pairs) we introduce a new structure --- the complex separation
that is separation of the complement of curve into two surfaces. In accordance
with Rokhlin terminology the complex separation is a complex topological
characteristic of real algebraic varieties. The complex separation is similar
to complex orientations introduced by O.Ya.Viro (to the absolute complex
orientation in the case when a curve is empty and to the relative complex
orientation otherwise). In some cases we calculate the complex separation of a
surface (for example in the case when surface is the double branched covering
of another surface along a curve). With the help of these calculations
applications of the extension of Rokhlin congruence gives some new restrictions
for complex orientations of curves on a hyperboloid.

34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
18
The categories of this paper are: econ
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn