  We investigate Lyman-$\alpha$ transmission spikes at $z > 5$ in synthetic
quasar spectra, and discuss their connection to the properties of the
intergalactic medium and their ability to constrain reionization models. We use
state-of-the-art radiation-hydrodynamic simulations from the Cosmic
Reionization On Computers series to predict the number of transmission spikes
as a function of redshift, both in the ideal case of infinite spectral
resolution and in a realistic observational setting. Transmission spikes are
produced in highly-ionized underdense regions located in the vicinity of UV
sources. We find that most of the predicted spikes are unresolved by current
observations, and show that our mock spectra are consistent with observations
of the quasar ULAS J1120+0641 in about 15% of the realizations. The spike
height correlates with both the gas density and the ionized fraction, but the
former link is erased when synthetic spectra are smoothed to realistically
achievable spectral resolutions. There exists a linear relationship between
spike width and the extent of the associated underdense region, with a slope
that is redshift-dependent. In agreement with observations, the spike
transmitted flux is suppressed at small distance from bright galaxies as these
reside in overdense regions. We argue that this anti-correlation can be used to
constrain large-scale density modes.
