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Explore the geometric and arithmetical aspects of K3-surfaces in this advanced mathematics lecture. Delve into the study of singular complex sextic curves, quartic surfaces, and smooth real ones through the lens of homological types. Discover the challenges that arise when combining singular real curves or surfaces and learn about a novel approach to address these issues for curves with empty real parts. Examine the equivariant equisingular deformation classification of real plane sextics with empty real parts, based on joint work with Alex Degtyarev. Gain insights into the intricate relationship between geometry and arithmetic in the context of complex algebraic geometry and real algebraic geometry.
