  We simulate the early stages of the evolution of turbulent, virialized,
high-mass protostellar cores, with primary attention to how cores fragment, and
whether they form a small or large number of protostars. Our simulations use
the Orion adaptive mesh refinement code to follow the collapse from ~0.1 pc
scales to ~10 AU scales, for durations that cover the main fragmentation phase,
using three-dimensional gravito-radiation hydrodynamics. We find that for a
wide range of initial conditions radiation feedback from accreting protostars
inhibits the formation of fragments, so that the vast majority of the collapsed
mass accretes onto one or a few objects. Most of the fragmentation that does
occur takes place in massive, self-shielding disks. These are driven to
gravitational instability by rapid accretion, producing rapid mass and angular
momentum transport that allows most of the gas to accrete onto the central star
rather than forming fragments. In contrast, a control run using the same
initial conditions but an isothermal equation of state produces much more
fragmentation, both in and out of the disk. We conclude that massive cores with
observed properties are not likely to fragment into many stars, so that, at
least at high masses, the core mass function probably determines the stellar
initial mass function. Our results also demonstrate that simulations of massive
star forming regions that do not include radiative transfer, and instead rely
on a barotropic equation of state or optically thin heating and cooling curves,
are likely to produce misleading results.
