Primer comprising a mixture G, in dispersion or solution in one or more solvents, of at least one copolymer obtained by copolymerizing a monomer mixture comprising at least 90 wt % of the following monomers: vinylcaprolactam and/or vinylpyrrolidone and one or more monomers a) and/or b): a) acrylic esters of a linear, primary alcohol having 2 to 10 carbon atoms in the alkyl radical of the alcohol, b) acrylic esters of a branched non-cyclic alcohol having 3 to 12 carbon atoms in the alkyl radical of the alcohol, at least one organofunctional silane of the general structure (I): (R1O—)xSi(R2)y(R3)z, at least one metal compound selected from the group consisting of metal acetylacetonates, metal alkoxides and alkoxy-metal acetylacetonates.