  The connections among galaxies, the dark matter halos where they form and the
properties of the large-scale Cosmic Web still need to be completely
disentangled. We use the cosmological hydrodynamical simulation TNG100 of the
IllustrisTNG suite to quantify the effects played by the large-scale density
field and the Cosmic Web morphology on the relation between halo mass and
galaxy stellar mass. We select objects with total dynamical mass in the range
$\geq 6.3\times 10^{10} h ^{-1}\, M_{\odot}$ up to a few $10^{14} h^{-1} \,
M_{\odot}$ between redshift $z=4$ and redshift $z=0$. A Cosmic Web class (knot,
filament, sheet, void) is assigned to each region of the volume using a density
field deformation tensor-based method. We find that galaxy stellar mass
strongly correlates with total dynamical mass and formation time, and more
weakly with large-scale overdensity and Cosmic Web class. The latter two
quantities correlate with each other, but are not entirely degenerate.
Furthermore, we find that at fixed halo mass, galaxies with stellar mass lower
than the median value are more likely to be found in voids and sheets, whereas
galaxies with stellar mass higher than the median are more likely to be found
in filaments and knots. Finally, we find that the dependence on environment is
stronger for satellites than for centrals, and discuss the physical
implications of these results.
