Abstract
For families of K3 surfaces, we establish a sufficient criterion for real or complex multiplication. Our criterion is arithmetic in nature. It may show, at first, that the generic fibre of the family has a nontrivial endomorphism field. Moreover, the endomorphism field does not shrink under specialization. As an application, we present two explicit families of K3 surfaces having real multiplication by Q( 2) and Q( 5), respectively.
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