# Real algebraic curves in real del Pezzo surfaces

Abstract : 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.
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https://tel.archives-ouvertes.fr/tel-02270776
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Submitted on : Monday, August 26, 2019 - 11:42:07 AM
Last modification on : Thursday, August 29, 2019 - 10:04:32 AM

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• HAL Id : tel-02270776, version 1

### Citation

Matilde Manzaroli. Real algebraic curves in real del Pezzo surfaces. Algebraic Geometry [math.AG]. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLX017⟩. ⟨tel-02270776⟩

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