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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., Comment: 14 pages, 8 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society