  We study the phase diagram of interacting electrons in a dispersionless Chern
band as a function of their filling. We find hierarchy multiplets of
incompressible states at fillings \nu=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well
as \nu=1/5,2/7. These are accounted for by an analogy to Haldane
pseudopotentials extracted from an analysis of the two-particle problem.
Important distinctions to standard fractional quantum Hall physics are
striking: absent particle-hole symmetry in a single band, an
interaction-induced single-hole dispersion appears, which perturbs and
eventually destabilizes incompressible states as \nu increases. For this reason
the nature of the state at \nu=2/3 is hard to pin down, while \nu=5/7,4/5 do
not seem to be incompressible in our system.
