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Let E and E' be elliptic curves over Q with complex multiplication by thering of integers of an imaginary quadratic field K and let Y=Kum(ExE') be theminimal desingularisation of the quotient of ExE' by the action of -1. We studythe Brauer groups of such surfaces Y and use them to furnish new examples oftranscendental Brauer-Manin obstructions to weak approximation.

Transcendental Brauer-Manin obstructions on singular K3 surfaces