  We present a theoretical study of the dynamical spin susceptibility for the
intriguing Fe-based superconductor FeSe, based on a tight-binding model
developed to account for the temperature-dependent band structure in this
system. The model allows for orbital ordering in the $d_{xz}/d_{yz}$ channel
below the structural transition and presents a strongly $C_4$ symmetry broken
Fermi surface at low temperatures which accounts for the nematic properties of
this material. The calculated spin excitations are peaked at wave vector
$(\pi,0)$ in the 1-Fe Brillouin zone, with a broad maximum at energies of order
a few meV. In this range, the occurrence of superconductivity sharpens this
peak in energy, creating a $(\pi,0)$ "neutron resonance" as seen in recent
experiments. With the exception of the quite low energy scale of these
fluctuations, these results are roughly similar to standard behavior in Fe
pnictide systems. At higher energies, however, intensity increases and shifts
to wave vectors along the $(\pi,0)$ - $(\pi,\pi)$ line. We compare with
existing inelastic neutron experiments and NMR data, and give predictions for
further studies.
