  Using toric Cartan matrices as abelian gauge charges, we present a class of
stringy fractional quantum Hall effect (FQHE) producing some recent
experimental observed filling factor values. More precisely, we derive the
corresponding Chern-Simons type models from M-theory compactified on four
complex dimensional hyper-K\"{a}hler manifolds X^4. These manifolds, which are
viewed as target spaces of a particular N=4 sigma model in two dimensions, are
identified with the cotangent bundles over intersecting 2-dimensional toric
varieties V_i^2 according to toric Cartan matrices. Exploring results of string
dualities, the presented FQHE can be obtained from D6-banes wrapping on such
intersecting toric varieties interacting with R-R gauge fields. This string
theory realization provides a geometric interpretation of the filling factors
in terms of toric and Euler characteristic topological data of the compactified
geometry. Concretely, explicit bilayer models are worked out in some details.
