Complex multiplication, rationality and mirror symmetry for abelian varieties

Details Complex multiplication, rationality and mirror symmetry for abelian varieties Complex multiplication, rationality and mirror symmetry for abelian varieties

2005-12-20

arxiv.org/abs/math/0512470v2

J.Geom.Phys.58:633-653,2008

Mathematics

Algebraic Geometry

22 pages, introduction and exposition of results rewritten, references added

Scientific paper

10.1016/j.geomphys.2008.01.001

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.

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