Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes about a combinatorial expression of the fundamental second kind
  differential on an algebraic curve   The zero locus of a bivariate polynomial $P(x,y)=0$ defines a compact Riemann
surface $\Sigma$. The fundamental second kind differential is a symmetric
$1\otimes 1$ form on $\Sigma\times \Sigma$ that has a double pole at coinciding
points and no other pole. As its name indicates, this is one of the most
important geometric objects on a Riemann surface. Here we give a rational
expression in terms of combinatorics of the Newton's polygon of $P$, involving
only integer combinations of products of coefficients of $P$. Since the
expression uses only combinatorics, the coefficients are in the same field as
the coefficients of $P$.

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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas