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The production of charmonia in the antiproton-nucleus reactions at plab = 3 − 10 GeV/c is studied within the Glauber model and the generalized eikonal approximation. The main reaction channel is charmonium formation in an antiproton-proton collision. The target mass dependence of the charmonium transparency ratio allows to determine the charmonium-nucleon cross section. The polarization effects in the production of χc2 states are evaluated.