  This work presents a methodological approach to generate realistic
$\gamma$-ray light curves of pulsars, resembling reasonably well the
observational ones observed by the Fermi-Large Area Telescope instrument,
fitting at the same time their high-energy spectra. The theoretical light
curves are obtained from a spectral and geometrical model of the
synchro-curvature emission. Despite our model relies on a few effective
physical parameters, the synthetic light curves present the same main features
observed in the observational $\gamma$-ray light curve zoo, such as the
different shapes, variety in the number of peaks, and a diversity of peak
widths. The morphological features of the light curves allows us to
statistically compare the observed properties. In particular, we find that the
proportion on the number of peaks found in our synthetic light curves is in
agreement with the observational one provided by the third Fermi-LAT pulsar
catalog. We also found that the detection probability due to beaming is much
higher for orthogonal rotators (approaching 100%) than for small inclination
angles (less than 20%).The small variation on the synthetic skymaps generated
for different pulsars indicates that the geometry dominates over timing and
spectral properties in shaping the gamma-ray light curves. This means that
geometrical parameters like the inclination angle can be in principle
constrained by gamma-ray data alone independently on the specific properties of
a pulsar. At the same time, we find that $\gamma$-ray spectra seen by different
observers can slightly differ, opening the door to constraining the viewing
angle of a particular pulsar.
