A polymer comprising recurring units having the formula (a), recurring units of at least one type selected from recurring units having the formula (b1') and recurring units having the formula (b2'), recurring units of at least one type selected from recurring units having the formula (c), and recurring units having the formula (d), and recurring units having the formula (e), wherein the formulae are as follows: wherein R A is hydrogen or methyl, R 1 and R 2 are each independently hydrogen or a C 1 -C 15 primary or secondary alkyl group in which some hydrogen may be substituted by a hydroxyl or C 1 -C 6 alkoxy moiety, or R 1 and R 2 may bond together to form a ring with the carbon atom to which they are attached, k 1 is 0 or 1, and k 2 is an integer of 2 to 4, wherein R B is hydrogen, fluorine, methyl or trifluoromethyl, A 1 is a single bond or a C 1 -C 10 alkanediyl group which may contain an ether bond, A 2 is a single bond or a C 1 -C 10 alkanediyl group which may contain an ether bond, with the proviso that A 2 is a single bond in case of d4=0, A 3 is a single bond or a C 1 -C 10 (d3+1)-valent aliphatic hydrocarbon group which may contain fluorine, ether bond, carbonyl moiety or carbonyloxy moiety, Rf 1 and Rf 2 are each independently a C 1 -C 6 alkyl group having at least one fluorine, Rf 1 may bond with A 3 to form a ring with the atom intervening therebetween, R 13 and R 14 are each independently a halogen atom, optionally halogenated C 2 -C 8 acyloxy group, optionally halogenated C 1 -C 6 alkyl group, or optionally halogenated C 1 -C 6 alkoxy group, t1 is 0 or 1, x1 and x2 are each independently an integer of 0 to 2, c1 is an integer satisfying 0 ≤ c1 ≤ 5+2 -c2, c2 is an integer of 1 to 3, d1 is an integer satisfying 0 ≤ d1 ≤ 5+2 -d2, d2 is 1 or 2, d3 is 1 or 2, d4 is 0 or 1, t2 is 0 or 1, t2 being 1 in case of d4=0, wherein R B is hydrogen, fluorine, methyl or trifluoromethyl, R 15 and R 16 are each independently a halogen atom, optionally halogenated C 2 -C 8 acyloxy group, optionally halogenated C 1 -C 6 alkyl group, or optionally halogenated C 1 -C 6 alkoxy group, R 17 is an acetyl, acetoxy, C 1 -C 20 alkyl, C 1 -C 20 primary alkoxy, C 2 -C 20 secondary alkoxy, C 2 -C 20 acyloxy, C 2 -C 20 alkoxyalkyl, C 2 -C 20 alkylthioalkyl, halogen, nitro or cyano group, A 4 is a single bond or a C 1 -C 10 alkanediyl group which may contain an ether bond, e is an integer of 0 to 5, f is an integer of 0 to 3, g is an integer of 0 to 5, t3 is 0 or 1, and x3 is an integer of 0 to 2. A 1 is a single bond or a C 1 -C 10 alkanediyl group which may contain an ether bond, A 2 is a single bond or a C 1 -C 10 alkanediyl group which may contain an ether bond, with the proviso that A 2 is a single bond in case of d4=0, A 3 is a single bond or a C 1 -C 10 (d3+1)-valent aliphatic hydrocarbon group which may contain fluorine, ether bond, carbonyl moiety or carbonyloxy moiety, Rf 1 and Rf 2 are each independently a C 1 -C 6 alkyl group having at least one fluorine, Rf 1 may bond with A 3 to form a ring with the atom intervening therebetween, R 13 and R 14 are each independently a halogen atom, optionally halogenated C 2 -C 8 acyloxy group, optionally halogenated C 1 -C 6 alkyl group, or optionally halogenated C 1 -C 6 alkoxy group, t1 is 0 or 1, x1 and x2 are each independently an integer of 0 to 2, c1 is an integer satisfying 0 ≤ c1 ≤ 5+2 -c2, c2 is an integer of 1 to 3, d1 is an integer satisfying 0 ≤ d1 ≤ 5+2 -d2, d2 is 1 or 2, d3 is 1 or 2, d4 is 0 or 1, t2 is 0 or 1, t2 being 1 in case of d4=0, wherein R B is hydrogen, fluorine, methyl or trifluoromethyl, R 15 and R 16 are each independently a halogen atom, optionally halogenated C 2 -C 8 acyloxy group, optionally halogenated C 1 -C 6 alkyl group, or optionally halogenated C 1 -C 6 alkoxy group, R 17 is an acetyl, acetoxy, C 1 -C 20 alkyl, C 1 -C 20 primary alkoxy, C 2 -C 20 secondary alkoxy, C 2 -C 20 acyloxy, C 2 -C 20 alkoxyalkyl, C 2 -C 20 alkylthioalkyl, halogen, nitro or cyano group, A 4 is a single bond or a C 1 -C 10 alkanediyl group which may contain an ether bond, e is an integer of 0 to 5, f is an integer of 0 to 3, g is an integer of 0 to 5, t3 is 0 or 1, and x3 is an integer of 0 to 2. R 15 and R 16 are each independently a halogen atom, optionally halogenated C 2 -C 8 acyloxy group, optionally halogenated C 1 -C 6 alkyl group, or optionally halogenated C 1 -C 6 alkoxy group, R 17 is an acetyl, acetoxy, C 1 -C 20 alkyl, C 1 -C 20 primary alkoxy, C 2 -C 20 secondary alkoxy, C 2 -C 20 acyloxy, C 2 -C 20 alkoxyalkyl, C 2 -C 20 alkylthioalkyl, halogen, nitro or cyano group, A 4 is a single bond or a C 1 -C 10 alkanediyl group which may contain an ether bond, e is an integer of 0 to 5, f is an integer of 0 to 3, g is an integer of 0 to 5, t3 is 0 or 1, and x3 is an integer of 0 to 2.