Real Plane Sextic Curves Without Real Singular Points

Explore the topology of real algebraic curves through this mathematical lecture focusing on degree 6 curves in the real projective plane. Begin with a foundational introduction to the topology of real algebraic curves before delving into the specific case of sextic curves. Discover how the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, including the polarization, exceptional divisors, and real structure recorded in the homology of the covering K3-surface. Learn about an Arnold-Gudkov-Rokhlin type congruence for real algebraic curves and surfaces with certain singularities. This presentation was recorded during the thematic meeting "Jean Morlet Chair - Real algebraic geometry and Birational geometry" at the Centre International de Rencontres Mathématiques in Marseille, France, providing advanced insights into the intersection of real algebraic geometry and topological analysis.