  After the end of inflation, the inflaton field oscillates around a local
minimum of its potential and decays into ordinary matter. These oscillations
trigger a resonant instability for cosmological perturbations with wavelengths
that exit the Hubble radius close to the end of inflation. In this paper, we
study the formation of Primordial Black Holes (PBHs) at these enhanced scales.
We find that the production mechanism can be so efficient that PBHs
subsequently dominate the content of the universe and reheating proceeds from
their evaporation. Observational constraints on the PBH abundance also restrict
the duration of the resonant instability phase, leading to tight limits on the
reheating temperature that we derive. We conclude that the production of PBHs
during reheating is a generic and inevitable property of the simplest
inflationary models, and does not require any fine tuning of the inflationary
potential.
