Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Patchworking real algebraic varieties   Patchworking is a construction of a one-parameter family of real algebraic
hypersurfaces. For sufficiently small positive values of the parameter, the
hypersurfaces can be obtained by gluing of given hypersurfaces topologically.
The author invented patchworking in 1979-81 and used it for constructing of
real plane algebraic curves with complicated prescribed topology. In
particular, it helped to complete isotopy classification of nonsingular plane
projective real algebraic curves of degree 7. A special case of the
patchworking, combinatorial patchworking, can be considered as Litvinov-Maslov
quantization of a tropical variety. Due to its simplicity, combinatorial
patchworking is better known than the general one. This paper is the original
presentation of the patchworking, in its full generality.

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg