Using a sample of 81 galactic, detached eclipsing binary stars we investigated the global zero-point shift of their parallaxes with the Gaia Data Release 2 (DR2) parallaxes. The stars in the sample lay in a distance range of 0.04-2 kpc from the Sun. The photometric parallaxes {pi}_Phot of the eclipsing binaries were determined by applying a number of empirical surface brightness - color (SBC) relations calibrated on optical-infrared colors. For each SBC relation we calculated the individual differences d{pi}_i = ({pi}_Gaia - {pi}_Phot)_i and then we calculated unweighted and weighted means. As the sample covers the whole sky we interpret the weighted means as the global shifts of the Gaia DR2 parallaxes with respect to our eclipsing binary sample. Depending on the choice of the SBC relation the shifts vary from -0.094 mas to -0.025 mas. The weighted mean of the zero-point shift from all colors and calibrations used is d{pi} = -0.054 +/- 0.024 mas. However, the SBC relations based on (B-K) and (V-K) colors, which are the least reddening dependent and have the lowest intrinsic dispersions, give a zero-point shift of d{pi} = -0.031 +/- 0.011 mas in full agreement with results obtained by Lindegren et al. and Arenou et al. Our result confirms the global shift of Gaia DR2 parallaxes of d{pi} = -0.029 mas reported by the Gaia team, but we do not confirm the larger zero-point shift reported by a number of follow-up papers.
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