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An element in the Brauer group of a general complex projective K3 surface S defines a sublattice of the transcendental lattice of S. We consider those elements of prime order for which this sublattice is Hodge-isometric to the transcendental lattice of another K3 surface X. We recall that this defines a finite map between moduli spaces of polarized K3 surfaces and we compute its degree. We show how the Picard lattice of X determines the Picard lattice of S in the case that the Picard number of X is two.
Galluzzi et al. (Thu,) studied this question.