  We show that under a suitable transversality condition, the intersection of
two rational subtori in an algebraic torus $(\C^*)^n$ is a finite group which
can be determined using the torsion part of some associated lattice.
Applications are given to the study of characteristic varieties of smooth
complex algebraic varieties. As an example we discuss A. Suciu's line
arrangement, the so-called deleted $B_3$-arrangement.

Algebraic Geometry;Geometric Topology