A polymer comprising a structural unit represented by the formula (Ia) or (Ib): wherein R1 represents a hydrogen atom etc., R2 represents a linear, branched chain or cyclic C1-C8 alkyl group, R3 represents a methyl group, n represents an integer of 0 to 14, Z1 represents a single bond etc., k represents an integer of 1 to 4, R4 and R5 each independently represents a hydrogen atom etc., and m represents an integer of 1 to 3, a structural unit represented by the formula (II): wherein R6 and R7 each independently represents a hydrogen atom etc., R8 represents a methyl group, R9 represents a hydrogen atom etc., n′ represents an integer of 0 to 12, Z2 represents a single bond etc., k′ represents an integer of 1 to 4, R21 and R22 each independently represents a hydrogen atom etc., and R23 represents a C1-C30 monovalent hydrocarbon group, and at least one structural unit selected from the group consisting of structural units represented by the formulae (IIIa), (IIIb), (IIIc), (IIId) and (IIIf) wherein R10 represents a hydrogen atom etc., R11 represents a methyl group, R12 is independently in each occurrence a carboxyl group etc., j represents an integer of 0 to 3, a represents an integer of 0 to 5, b represents an integer of 0 to 3, c represents an integer of 0 to (2j+2), Z3 represents a single bond etc., and k″ represents an integer of 1 to 4.