Seminar Algebra and Geometry: Matilde Manzaroli (École Polytechnique and Université de Nantes)

Real algebraic curves in real minimal del Pezzo surfaces

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 the real projective plane 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 the real projective space, 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 real minimal surfaces. In this talk, we present some results about the classification of topological types realized by real algebraic curves in real minimal del Pezzo surfaces of degree.

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