A polymer, which contains a structural unit having a carboxyl group represented by the following formula (1) at a side chain of the structural unit, wherein node position is formed, when the polymer is dissolved in an alkali aqueous solution having a pH of 10 or more and kept at 25.degree. C. for 60 days: ##STR00001## wherein R.sup.1 represents a hydrogen atom or a methyl group; R.sup.2 represents an (n+1)-valent organic linking group containing an ester group represented by --O(C.dbd.O)--; A represents an oxygen atom or NR.sup.3--; R.sup.3 represents a hydrogen atom, or an monovalent hydrocarbon group having from 1 to 10 carbon atoms; and n indicates an integer of from 1 to 5.