三角曲线的一个无凸性假设的Viro定理

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 pos…