2020/02/01 by Elsenhans, Andreas-Stephan, Jahnel, Jörg
#11T06 secondary #14F20 #14F25 #14J10 #14J20 #14J28 primary #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2002.00233
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 specialisation. As an application, we present two explicit families of K3 surfaces having real multiplication by \bbQ(√(2)) and \bbQ(√(5)), respectively.