  The hypothesis of a universal initial mass function (IMF) -- motivated by
observations in nearby stellar systems -- has been recently challenged by the
discovery of a systematic variation of the IMF with the central velocity
dispersion, {\sigma}, of early-type galaxies (ETGs), towards an excess of
low-mass stars in high-{\sigma} galaxies. This trend has been derived so far
from integrated spectra, and remains unexplained at present. To test whether
such trend depends on the local properties within a galaxy, we have obtained
new, extremely deep, spectroscopic data, for three nearby ETGs, two galaxies
with high {\sigma} (~300 km/s), and one lower mass system, with {\sigma} ~ 100
km/s. From the analysis of IMF-sensitive spectral features, we find that the
IMF depends significantly on galactocentric distance in the massive ETGs, with
the enhanced fraction of low-mass stars f mostly confined to their central
regions. In contrast, the low-{\sigma} galaxy does not show any significant
radial gradient in the IMF, well described by a shallower distribution,
relative to the innermost regions of massive galaxies, at all radii. Such a
result indicates that the IMF should be regarded as a local (rather than
global) property, and suggests a significant difference between the formation
process of the core and the outer regions of massive ETGs.
