Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: M-curves of degree 9 with three nests   The first part of Hilbert's sixteenth problem deals with the classification
of the isotopy types realizable by real plane algebraic curves of a given
degree $m$. For $m = 9$, the classification of the $M$-curves is still wide
open. Let $C_9$ be an $M$-curve of degree 9 and $O$ be a non-empty oval of
$C_9$. If $O$ contains in its interior $\alpha$ ovals that are all empty, we
say that $O$ together with these $\alpha$ ovals forms a nest. The present paper
deals with the $M$-curves with three nests. Let $\alpha_i, i = 1, 2, 3$ be the
numbers of empty ovals in each nest. We prove that at least one of the
$\alpha_i$ is odd. This is a step towards a conjecture of A. Korchagin,
claiming that at least two of the $\alpha_i$ should be odd.

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci