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For a change, I will give a detailed proof of one of our joint results announced in an earlier talk, viz. the fact that the equisingular equivariant deformation type of a real plane sextic curve with smooth real part is determined by its real homological type (in the most naïve meaning of the term); this theorem has been used to obtain a complete classification of such curves. The principal goal is introducing the newer generation into the fascinating theory of K3-surfaces, real aspects thereof, and algebra/number theory involved.