  We study perturbations of a complex scalar field during reheating with no
self-interaction in the regime $\mu \gg H$, when the scalar field has a fast
oscillatory behaviour (close to a pressure-less fluid). We focus on the precise
determination of the instability scale and look at the probability that
unstable fluctuations may form Primordial Black Holes (PBHs). After deriving
such probability, we impose restrictions on the duration of the fast
oscillations period by looking at constraints to the abundance of PBHs via
Planck relics.
