Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of $C^{(n)}$   In this paper a new geometric characterization of the $n$th symmetric product
of a curve is given. Specifically, we assume that there exists a chain of
smooth subvarieties $V_i$ of dimension $i$, such that $V_i$ is an ample divisor
in $V_{i+1}$ and its intersection product with $V_1$ is one. That the Albanese
dimension of $V_2$ is $2$ and the genus of $V_1$ is equal to the irregularity
of the variety. We prove that in this case the variety is isomorphic to the
symmetric product of a curve.

25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc