%0 Journal Article
%T Complex multiplication, rationality and mirror symmetry for abelian varieties
%A Meng Chen
%J Mathematics
%D 2005
%I arXiv
%R 10.1016/j.geomphys.2008.01.001
%X We show that complex multiplication on abelian varieties is equivalent to the existence of a constant rational K\"ahler metric. We give a sufficient condition for a mirror of an abelian variety of CM-type to be of CM-type as well. We also study the relationship between complex multiplication and rationality of a toroidal lattice vertex algebra.
%U http://arxiv.org/abs/math/0512470v2