Complex multiplication, rationality and mirror symmetry for abelian varieties
Algebraic Geometry
2008-11-26 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0512470,
title = {Complex multiplication, rationality and mirror symmetry for abelian varieties},
author = {Meng Chen},
journal= {arXiv preprint arXiv:math/0512470},
year = {2008}
}
Comments
22 pages, introduction and exposition of results rewritten, references added