  Fractional Chern insulators realize the remarkable physics of the fractional
quantum Hall effect (FQHE) in crystalline systems with Chern bands. The lowest
Landau level (LLL) is known to host the FQHE, but not all Chern bands are
suitable for realizing fractional Chern insulators (FCI). Previous approaches
to stabilizing FCIs focused on mimicking the LLL through momentum space
criteria. Here instead we take a real-space perspective by introducing the
notion of vortexability. Vortexable Chern bands admit a fixed operator that
introduces vortices into any band wavefunction while keeping the state entirely
within the same band. Vortexable bands admit trial wavefunctions for FCI
states, akin to Laughlin states. In the absence of dispersion and for
sufficiently short ranged interactions, these FCI states are the ground state
-- independent of the distribution of Berry curvature. Vortexable bands are
much more general than the LLL, and we showcase a recipe for constructing them.
We exhibit diverse examples in graphene-based systems with or without magnetic
field, and with any Chern number. A special class of vortexable bands is shown
to be equivalent to the momentum space "trace condition" or "ideal band
condition". In addition, we also identify a more general form of vortexability
that goes beyond this criterion. We introduce a modified measure that
quantifies deviations from general vortexability which can be applied to
generic Chern bands to identify promising FCI platforms.
