  The IceCube evidence for cosmic neutrinos in the high-energy starting events
(HESE) sample has inspired a large number of hypothesis on their origin, mainly
due to the poor precision on the measurement of the direction of showering
events. The fact that most of HESE are downward going suggests a possible
Galactic component. This could be originated either by a single point-like
source or to a directional excess from an extended Galactic region. These
hypotheses are reviewed and constrained, using the present available upper
limits from the ANTARES neutrino telescope.
  ANTARES detects $\nu_\mu$ from sources in the Southern sky with an effective
area larger than that providing the IceCube HESE for $E_\nu<60$ TeV and a
factor of about two smaller at 1 PeV. The use of the $\nu_\mu$ signal enables
an accurate measurement of the incoming neutrino direction. The Galactic signal
allowed by the IceCube HESE and the corresponding ANTARES limits are studied in
terms of a power law flux $E^{-\Gamma}$, with spectral index $\Gamma$ ranging
from 2.0 to 2.5 to cover most astrophysical models.
