  Short GRBs are commonly thought to originate from the merging of double
compact object binaries but direct evidence for this scenario is still missing.
Optical observations of short GRBs allow us to measure redshifts, firmly
identify host galaxies, characterize their properties, and accurately localize
GRBs within them. Multiwavelength observations of GRB afterglows provide useful
information on the emission mechanisms at work. These are all key issues that
allow one to discriminate among different models of these elusive events. We
carried out photometric observations of the short/hard GRB 051227, GRB 061006,
and GRB 071227 with the ESO-VLT starting from several hours after the explosion
down to the host galaxy level several days later. For GRB 061006 and GRB 071227
we also obtained spectroscopic observations of the host galaxy. We compared the
results obtained from our optical observations with the available X-ray data of
these bursts. For all the three above bursts, we discovered optical afterglows
and firmly identified their host galaxies. About half a day after the burst,
the optical afterglows of GRB 051227 and GRB 061006 present a decay
significatly steeper than in the X-rays. In the case of GRB 051227, the optical
decay is so steep that it likely indicates different emission mechanisms in the
two wavelengths ranges. The three hosts are blue, star forming galaxies at
moderate redshifts and with metallicities comparable to the Solar one. The
projected offsets of the optical afterglows from their host galaxies centers
span a wide range, but all afterglows lie within the light of their hosts and
present evidence for local absorption in their X-ray spectra. We discuss our
findings in light of the current models of short GRB progenitors.
