Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distinguished varieties and the Nevanlinna-Pick interpolation problem on
  the symmetrized bidisk   Starting with a solvable Nevanlinna-Pick interpolation problem with the
initial data coming from the symmetrized bidisk, this paper studies the
corresponding uniqueness set, i.e., the largest set in the domain where all
solutions to the problem coincide. It is shown that the uniqueness set
coincides with an algebraic variety in the domain. The algebraic variety -
canonically constructed from the interpolation data - is called the uniqueness
variety. It was shown that the uniqueness variety contains a distinguished
variety which by definition is the zero set of a two-variable polynomial that
intersects the domain and exits through its distinguished boundary. A complete
algebraic and geometric characterizations of distinguished varieties are
obtained in this paper.

22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph