Ilia Itenberg: Real Plane Sextic Curves Without Real Singular Points

We will start with a brief introduction to topology of real algebraic curves, and then will discuss in more details the case of curves of degree 6 in the real projective plane. We will show that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, that is, the polarization, exceptional divisors, and real structure recorded in the homology of the covering K3-surface. We will also present an Arnold-Gudkov-Rokhlin type congruence for real algebraic curves/surfaces with certain singularities.

Recording during the thematic meeting : «Jean Morlet Chair - Real algebraic geometry and Birational geometry » the June 02, 2025 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker : Luca Récanzone

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