%0 Journal Article
%T Abelian surfaces with an automorphism and quaternionic multiplication
%A Matteo A. Bonfanti
%A Bert van Geemen
%J Mathematics
%D 2014
%I arXiv
%X We construct one dimensional families of Abelian surfaces with quaternionic multiplication which also have an automorphism of order three or four. Using Barth's description of the moduli space of (2,4)-polarized Abelian surfaces, we find the Shimura curve parametrizing these Abelian surfaces in a specific case. We explicitly relate these surfaces to the Jacobians of genus two curves studied by Hashimoto and Murabayashi. We also describe a (Humbert) surface in Barth's moduli space which parametrizes Abelian surfaces with real multiplication by Z[\sqrt{2}].
%U http://arxiv.org/abs/1408.1267v1