Some remarks on Brauer Classes of K3-type

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.