Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic pointed quartic curves in $\mathbb{R}\mathbb{P}^{2}$ and
  uninodal dessins   In this article we obtain a rigid isotopy classification of generic pointed
quartic curves $(A,p)$ in $\mathbb{R}\mathbb{P}^{2}$ by studying the
combinatorial properties of dessins. The dessins are real versions, proposed by
S. Orevkov, of Grothendieck's dessins d'enfants.
  This classification contains 20 classes determined by the number of ovals of
$A$, the parity of the oval containing the marked point $p$, the number of
ovals that the tangent line $T_p A$ intersects, the nature of connected
components of $A\setminus T_p A$ adjacent to $p$, and in the maximal case, on
the convexity of the position of the connected components of $A\setminus T_p
A$.
  We study the combinatorial properties and decompositions of dessins
corresponding to real uninodal trigonal curves in real ruled surfaces. Uninodal
dessins in any surface with non-empty boundary can be decomposed in blocks
corresponding to cubic dessins in the disk $\mathbf{D}^2$, which produces a
classification of these dessins. The classification of dessins under
consideration leads to a rigid isotopy classification of generic pointed
quartic curves in $\mathbb{R}\mathbb{P}^{2}$. This classification was first
obtained by S. Rieken based on the relation between quartic curves and del
Pezzo surfaces.

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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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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: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph