  We investigate the gravitational production of scalar dark matter particles
during the inflationary and reheating epochs. The oscillatory behavior of the
curvature scalar $R$ during the reheating phase generates two different
enhancement mechanisms in the particle production. On the one hand, as it has
been already discussed in previous works, it induces tachyonic instabilities in
the field which are the dominant enhancement mechanism for light masses. On the
other hand, we have found that it also provokes a resonant effect in the
ultraviolet region of the spectrum which becomes dominant for masses in the
range $10^9\,{\rm GeV}$ to $10^{13}\,{\rm GeV}$. We have developed an
analytical approximation to describe this resonance effect and its consequences
on the ultraviolet regime. Once we have calculated the theoretical
gravitational production, we constrain the possible values of the
phenomenological field parameters to be considered as a dark matter candidate.
We do so by comparing the theoretically predicted abundance with the observed
one and ensuring that the theoretical prediction does not lead to
overproduction. In particular, we find that there is a region of intermediate
masses that is forbidden as they would lead to overproduction.
