  We study scaling of the ground-state fidelity in neighborhoods of quantum
critical points in a model of interacting spinfull fermions - a BCS-like model.
Due to the exact diagonalizability of the model, in one and higher dimensions,
scaling of the ground-state fidelity can be analyzed numerically with great
accuracy, not only for small systems but also for macroscopic ones, together
with the crossover region between them. Additionally, in one-dimensional case
we have been able to derive a number of analytical formulae for fidelity and
show that they accurately fit our numerical results; these results are reported
in the article. Besides regular critical points and their neighborhoods, where
well-known scaling laws are obeyed, there is the multi-critical point and
critical points in its proximity where anomalous scaling behavior is found. We
consider also scaling of fidelity in neighborhoods of critical points where
fidelity oscillates strongly as the system size or the chemical potential is
varied. Our results for a one-dimensional version of a BCS-like model are
compared with those obtained by Rams and Damski in similar studies of a quantum
spin chain - an anisotropic XY model in transverse magnetic field.
