Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether–Lefschetz loci

We describe the Hodge theory of brilliant families K3 surfaces. Their characteristic feature is a close link between structures any two fibres over points in Noether–Lefschetz locus. Twistor deformations, analytic Tate–Šafarevič group, and certain one-dimensional Shimura special cycles are covered by theory. In this setting, Brauer group viewed as locus family or specialization loci approaching twistor spaces. Passing from one algebraic fibre to another, which construction transcendental operation, here first deforming along more then