  Primordial black holes (PBH) can form in the early Universe from peaks of the
primordial curvature perturbations. The statistics of the peaks determines the
abundance of PBHs, and is related to the amplitude of the primordial curvature
spectrum. We study single field inflationary models with local features of the
inflaton potential which induce a growth of curvature perturbations on
super-horizon scales, which can increase the spectrum, and consequently the
predicted PBHs abundance. We compute the effects of the different parameters of
the features on the PBHs abundance, giving some example of models compatible
with observational constraints. The mechanism is general, and can induce the
PBH production in diffent mass ranges by appropriately tuning the parameters,
and we give a specific example producing PBHs with abundance compatible with
asteroid mass constraints.
