A polymer includes a first structural unit represented by formula (1-1), (1-2) or (1-3) and a second structural unit represented by formula (2) or (3). In the formulae (1-1) to (1-3), (2) and (3), R1, R10 and R11 each represent a halogen atom, a monovalent hydrocarbon group having 1 to 20 carbon atoms, a monovalent halogenated hydrocarbon group having 1 to 20 carbon atoms, a nitro group or a cyano group; Zs each represent —O— or —S—; R4s each represent a methylene group or an alkylene group having 2 to 4 carbon atoms; and L represents a divalent group represented by formula (2-1). In the formula (2-1), Ra represents a divalent alicyclic hydrocarbon group having 5 to 30 ring atoms or a divalent fluorinated alicyclic hydrocarbon group having 5 to 30 ring atoms.