  We compute the probability density distribution of maxima for a scalar random
field in the presence of local non-gaussianities. The physics outcome of this
analysis is the following. If we focus on maxima whose curvature is larger than
a certain threshold for gravitational collapse, our calculations illustrate how
the fraction of the Universe's mass in the form of primordial black holes
(PBHs) changes in the presence of local non-gaussianities. We find that
previous literature on the subject exponentially overestimate, by many orders
of magnitude, the impact of local non-gaussianities on the PBH abundance. We
explain the origin of this discrepancy, and conclude that, in realistic
single-field inflationary models with ultra slow-roll, one can obtain the same
abundance found with the gaussian approximation simply changing the peak
amplitude of the curvature power spectrum by no more than a factor of two. We
comment about the relevance of non-gaussianities for second-order gravitational
waves.
