The invention relates to novel crosslinkable copolymers which are obtainable by (a) copolymerizing at least two different hydrophilic monomers selected from the group consisting of N,N-dimethyl acrylamide (DMA), 2-hydroxyethyl acrylate (HEA), glycidyl methacrylate (GMA), N-vinylpyrrolidone (NVP), acrylic acid (AA) and a C1-C4-alkoxy polyethylene glycol (meth)acrylate having a weight average molecular weight of from 200 to 1500, and at least one crosslinker comprising two or more ethylenically unsaturated double bonds in the presence of a chain transfer agent having a functional group; and (b) reacting one or more functional groups of the resulting copolymer with an organic compound having an ethylenically unsaturated group.