We present BVRI photometry and spectrophotometry of GRB 990510 obtained wit
h the ESO VLT/Antu telescope during the late decline phase. Between days 8
and 29 after the burst, the afterglow faded from R = 24.2 to similar to 26.
4. The spectral flux distribution and the light curve support the interpret
ation of the afterglow as synchrotron emission from a jet. The light curve
is consistent with the optical transient alone but an underlying SN with ma
ximum brightness R > 27.4 or a galaxy with R > 27.6 (3-sigma upper limits)
cannot be ruled out. To a 5-sigma detection threshold of R = 26.1, no galax
y is found within 6 " of the transient. A very blue V similar or equal to 2
4.5 extended object which may qualify as a starburst galaxy is located 12 "
SE, but at unknown redshift.