Modular map for the family of abelian surfaces via elliptic K3 surfaces

In this paper we give explicit modular maps for the family of abelian surfaces and that of the abelian surfaces whose endomorphism algebra contains Zinverted right perpendicular (1 + root 5)/2inverted left perpendicular. We obtain a description of the Shimura variety for the latter family, also. The notion of the family of K3 surfaces with a fixed marking plays a central role. As the basement of our study we use the expressions of those families given by Clingher-Doran, A. Nagano and the work of A. Kumar as well. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim