English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article we obtain the rigid isotopy classification of genericrational curves of degre $5$ in $\mathbb{R}\mathbb{P}^{2}$. In order to studythe rigid isotopy classes of nodal rational curves of degree $5$ in$\mathbb{R}\mathbb{P}^{2}$, we associate to every real rational nodal quinticcurve with a marked real nodal point a nodal trigonal curve in the Hirzebruchsurface $\Sigma_3$ and the corresponding nodal real dessin on$\mathbb{C}\mathbb{P}^{1}/(z\mapsto\bar{z})$. The dessins are real versions,proposed by S. Orevkov, of Grothendieck's dessins d'enfants. The dessins aregraphs embedded in a topological surface and endowed with a certain additionalstructure.  We study the combinatorial properties and decompositions of dessinscorresponding to real nodal trigonal curves $C\subset \Sigma_n$ in realHirzebruch surfaces $\Sigma_n$. Nodal dessins in the disk can be decomposed inblocks corresponding to cubic dessins in the disk $\mathbf{D}^2$, whichproduces a classification of these dessins. The classification of dessins underconsideration leads to a rigid isotopy classification of real rational quinticsin $\mathbb{R}\mathbb{P}^{2}$.

Rigid isotopy classification of generic rational quintics in $\mathbb{R}\mathbb{P}^{2}$