The study of the topology of real algebraic varieties dates back to the work of Harnack, Klein and Hilbert in the 19th century; in particular, the isotopy type classification of real algebraic curves with a fixed degree in RP2 is a classical subject that has undergone considerable evolution. On the other hand, apart from studies concerning Hirzebruch surfaces and at most degree 3 surfaces in RP3, not much is known for more general ambient surfaces. In particular, this is because varieties constructed using the patchworking method are hypersurfaces of toric varieties. However, there are many other real algebraic surfaces. Among these are the real rational surfaces, and more particularly the $mathbb{R}$-minimal surfaces. In this thesis, we extend the study of the topological types realized by real algebraic curves to the real minimal del Pezzo surfaces of degree 1 and 2. Furthermore, we end the classification of separating and non-separating real algebraic curves of bidegree $(5,5)$ in the quadric ellipsoid.

中文翻译：

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Real del Pezzo 曲面上的实代数曲线

对实代数簇拓扑的研究可以追溯到 19 世纪 Harnack、Klein 和 Hilbert 的工作；特别是RP2中具有固定阶数的实代数曲线的同位素类型分类是一个经历了相当大发展的经典课题。另一方面，除了关于 Hirzebruch 曲面和 RP3 中最多 3 阶曲面的研究之外，对于更一般的环境曲面知之甚少。特别是，这是因为使用拼凑方法构建的品种是复曲面品种的超曲面。然而，还有许多其他的实代数曲面。其中包括真正的有理曲面，尤其是 $mathbb{R}$-minimal 曲面。在这篇论文中，