Context :

Aims : The effect of frequency-dependent AGN core positions ( “ core-shifts ” ) on radio Very Long Baseline Interferometry ( VLBI ) global astrometry measurements is investigated .

Methods : The basic equations relating to VLBI astrometry are reviewed , including the effects of source structure .
A power-law representation of core-shifts , based on both observations and theoretical considerations of jet conditions , is incorporated .

Results : It is shown that , in the presence of core-shifts , phase and group-delay astrometry measurements yield different positions .
For a core displacement from the jet base parametrized by \Delta x ( \lambda ) = k \lambda ^ { \beta } , group delays measure a “ reduced ” core-shift of ( 1 - \beta ) \Delta x ( \lambda ) .
For the astrophysically-significant case of \beta = 1 , group delays measure no shift at all , giving the position of the jet base .
At 8.4 GHz an estimated typical offset between phase and group-delay positions of \sim 170 \mu as is smaller than the current \sim 250 \mu as precision of group-delay positions of the sources used to define the ICRF ; however , this effect must be taken into account for future measurements planned with improved accuracy when comparing with optical positions of AGN to be obtained with the GAIA mission .

Conclusions :