  Fast radio bursts are extragalactic radio transient events lasting a few
milliseconds with a ~Jy flux at ~1 GHz. We propose that these properties
suggest a neutron star progenitor, and focus on coherent curvature radiation as
the radiation mechanism. We study for which sets of parameters the emission can
fulfil the observational constraints. Even if the emission is coherent, we find
that self-absorption can limit the produced luminosities at low radio
frequencies and that an efficient re-acceleration process is needed to balance
the dramatic energy losses of the emitting particles. Self-absorption limits
the luminosities at low radio frequency, while coherence favours steep
optically thin spectra. Furthermore, the magnetic geometry must have a high
degree of order to obtain coherent curvature emission. Particles emit photons
along their velocity vectors, thereby greatly reducing the inverse Compton
mechanism. In this case we predict that fast radio bursts emit most of their
luminosities in the radio band and have no strong counterpart in any other
frequency bands.
