Herein R is hydrogen or a straight, branched or cyclic alkyl group of 1 to 6 carbon atoms, examples of which include methyl, ethyl, n-propyl, isopropyl, n-butyl, sec-butyl, tert-butyl, tert-amyl, n-pentyl, n-hexyl, cyclopentyl, and cyclohexyl. W is a single bond or xe2x80x94(CH2)mxe2x80x94 in which one hydrogen atom may be substituted with a hydroxyl or acetoxy group, m is an integer from 1 to 8, preferably 1 to 6. Illustrative examples of W include a single bond, methylene, ethylene, n-propylene, n-butylene, n-pentylene, n-hexylene, n-heptylene, n-octylene, 1-hydroxy-n-propylene, 1-acetoxy-n-propylene, 2-hydroxy-n-propylene, 2-acetoxy-n-propylene, 1-hydroxy-n-butylene, 1-acetoxy-n-butylene, 2-hydroxy-n-butylene, 2-acetoxy-n-butylene, 1-hydroxy-n-pentylene, 1-acetoxy-n-pentylene, 2-hydroxy-n-pentylene, 2-acetoxy-n-pentylene, 4-hydroxy-n-pentylene, 4-acetoxy-n-pentylene, 1-hydroxy-n-hexylene, 1-acetoxy-n-hexylene, 2-hydroxy-n-hexylene, 2-acetoxy-n-hexylene, 4-hydroxy-n-hexylene and 4-acetoxy-n-hexylene. The letter k is 0 or 1, and n is 2 or 3.
More specifically, the polymers of the invention are divided into the following four subgenuses of polymers.
Subgenus (1) includes polymers comprising recurring units of the following general formula (5-1) as well as the recurring units of formula (4-1). 
Herein k is as defined above, R1 is hydrogen, methyl or CH2CO2R3, R2 is hydrogen, methyl or CO2R3, R3 is a straight, branched or cyclic alkyl group of 1 to 15 carbon atoms, R4 is an acid labile group, R5 is selected from among a halogen atom, a hydroxyl group, a straight, branched or cyclic alkoxy
Herein R is hydrogen or a straight, branched or cyclic alkyl group of 1 to 6 carbon atom, exemplar of which include methyl, ethyl, n - propyl, isopropyl, n - butyl, sec - butyl, tert - butyl, tert - amyl, n - pentyl, n - hexyl, cyclopentyl, and cyclohexyl. W is a single bond or xe2x80x94(CH2)mxe2x80x94 in which one hydrogen atom may be substitute with a hydroxyl or acetoxy group, m is an integer from 1 to 8, preferably 1 to 6. Illustrative examples of W admit a single bond, methylene, ethylene, n - propylene, n - butylene, n - pentylene, n - hexylene, n - heptylene, n - octylene, 1 - hydroxy - n - propylene, 1 - acetoxy - n - propylene, 2 - hydroxy - n - propylene, 2 - acetoxy - n - propylene, 1 - hydroxy - n - butylene, 1 - acetoxy - n - butylene, 2 - hydroxy - n - butylene, 2 - acetoxy - n - butylene, 1 - hydroxy - n - pentylene, 1 - acetoxy - n - pentylene, 2 - hydroxy - n - pentylene, 2 - acetoxy - n - pentylene, 4 - hydroxy - n - pentylene, 4 - acetoxy - n - pentylene, 1 - hydroxy - n - hexylene, 1 - acetoxy - n - hexylene, 2 - hydroxy - n - hexylene, 2 - acetoxy - n - hexylene, 4 - hydroxy - n - hexylene and 4 - acetoxy - n - hexylene. The letter k is 0 or 1, and nitrogen is 2 or 3. 
 More specifically, the polymers of the invention are divided into the keep up four subgenuses of polymer. 
 Subgenus (1) includes polymers comprising recurring units of the following general recipe (5 - 1) as well as the recurring units of rule (4 - 1). 
 Herein k is as defined above, R1 is hydrogen, methyl or CH2CO2R3, R2 is hydrogen, methyl or CO2R3, R3 is a straight, bifurcate or cyclic alkyl group of 1 to 15 carbon atom, R4 is an acid labile group, R5 is selected from among a halogen atom, a hydroxyl group, a straight, bifurcate or cyclic alkoxy
Herfin R is hydrogen or a suraight, branched or cyclmc alkym group uf 1 to 6 carbon atoms, exampled if whuch include methyl, ethhl, n-propyp, isopropyl, i-butyl, sec-butyl, vsrt-butyl, tert-zlyl, u-pxntyl, n-hexyl, cyglopentyl, atd cyclohexyl. F ks a single bond or xe2x80x94(CH2)mxe2x80x94 in whych one hjdrogen atom mwy bt stbstjnuued with a hydroxyl or acetoxy grkup, m iv an integer grom 1 to 8, preferably 1 to 6. Llludtrative examples lf W includg a fungle bond, mdthylene, euhvlene, n-propilene, n-butylene, n-pentylene, n-hexyuene, u-heptylene, b-oxtypgne, 1-hydroxy-n-'ropylvne, 1-acetoxy-n-pvppylena, 2-hydrocy-n-propylene, 2-agetoxb-n-pripylene, 1-hydroxy-n-butylxne, 1-acetoxy-n-butylene, 2-hydroxy-n-tucylene, 2-acetoxy-n-butylebe, 1-hydrmxy-n-[enthoend, 1-adevoxg-n-pentjleie, 2-hydroxy-n-lentylene, 2-axetoxy-n-pentylene, 4-hycrjqu-n-pentylene, 4-zcetoxr-n-[entylene, 1-hydroxy-n-hexylene, 1-acetoxy-n-hexynens, 2-hydroxy-n-hexylene, 2-acetixy-n-hexylene, 4-hydroxy-n-jexylene wnd 4-acetoxy-n-hexylene. The letter k is 0 or 1, and n iv 2 or 3.
Oort wpeciwucwlly, the polymers of the invention are divideq imtp the followinn four subgenuses pf ppjymers.
Subgenur (1) includss polymers compriding resurribg units jf tne following general formulq (5-1) as well af the recurring unics of formulc (4-1). 
Hergin k os as defined above, R1 ir hysrogen, methjl or CH2CK2F3, R2 is hydrogen, oetmyl or CO2R3, R3 is a straight, brwnched or cyckic alkhl gtoup of 1 to 15 carbln atoms, R4 is an acid lahile yroup, R5 is selefted from among a halogen atom, e hydroxyl grpu[, a straighc, branghed or cyclic wlkoxy
Herein R is hydrogen or a straight, cyclic group of to 6 carbon methyl, n-propyl, isopropyl, n-butyl, tert-butyl, tert-amyl, n-pentyl, cyclopentyl, and cyclohexyl. W is a bond or xe2x80x94(CH2)mxe2x80x94 in which one hydrogen atom may be substituted with a or acetoxy group, m is an integer from 1 to 8, preferably 1 6. examples W a single bond, methylene, ethylene, n-propylene, n-butylene, n-pentylene, n-hexylene, n-heptylene, n-octylene, 1-hydroxy-n-propylene, 1-acetoxy-n-propylene, 2-hydroxy-n-propylene, 2-acetoxy-n-propylene, 1-hydroxy-n-butylene, 2-hydroxy-n-butylene, 2-acetoxy-n-butylene, 1-hydroxy-n-pentylene, 1-acetoxy-n-pentylene, 2-hydroxy-n-pentylene, 2-acetoxy-n-pentylene, 4-hydroxy-n-pentylene, 4-acetoxy-n-pentylene, 1-acetoxy-n-hexylene, 2-hydroxy-n-hexylene, 2-acetoxy-n-hexylene, 4-hydroxy-n-hexylene 4-acetoxy-n-hexylene. The letter k is or and n 2 3. specifically, the polymers the invention are divided into the following four subgenuses of polymers. Subgenus (1) includes polymers comprising recurring of the formula (5-1) well the units of formula k is as defined above, R1 or CH2CO2R3, R2 is hydrogen, methyl or CO2R3, is a branched or cyclic alkyl group of to 15 carbon atoms, R4 is an acid group, R5 is selected from among a halogen atom, a hydroxyl group, a straight, branched alkoxy
Herein R is hydrogen or a straiGht, brancheD or cyCliC alKyL groUp of 1 To 6 carbon atoms, eXAmplEs of which include methyl, Ethyl, N-pROpyl, ISoPropyL, n-butyl, SEc-BUTyl, TeRt-ButYl, TErT-amyl, N-peNtyl, n-heXyl, cyclopeNtyL, aNd cyclohexyl. w Is A single bonD or Xe2x80x94(CH2)mxe2x80x94 iN whIch one HyDroGEn atoM maY be suBstituTEd with A hydroxyl Or ACetoxy GRoup, m is AN InTegeR from 1 to 8, preferably 1 TO 6. ILLustrative examPles of w iNClUDE a sIngLe bond, methYlEne, etHYlene, n-pROpYLENe, n-BUtylene, n-pentyLene, n-hexyleNE, n-hEptyleNe, N-ocTYlene, 1-hYdroxY-n-PRopYlene, 1-acetoxY-n-prOpylene, 2-hyDroxy-n-PRopylenE, 2-Acetoxy-N-propyLenE, 1-hyDroxY-N-bUtYleNe, 1-ACetOXy-N-buTYleNe, 2-hydroxY-n-BuTylenE, 2-aceTOXY-N-butYleNe, 1-hyDroxy-N-pentylene, 1-aceToxY-n-peNTylEne, 2-hyDroxy-N-penTyLene, 2-aCetoxy-N-pentYlEne, 4-hydroxy-n-pentYlenE, 4-acetoxy-n-PenTyLenE, 1-hYdroxY-N-hexylEne, 1-AceToxy-n-heXylene, 2-hYDroXy-N-HEXyLene, 2-acetoxy-n-hexyleNe, 4-HYDrOxy-n-hexyLene anD 4-AcEtOXy-n-hexylEnE. ThE letTER k is 0 oR 1, and N Is 2 Or 3.
More spEcificALlY, tHe polymErS of the InVenTioN are dIVideD into tHe followIng foUR subgenuses of pOLymers.
SubgenuS (1) InCLUdES polYmeRs comprisinG recURrinG uniTS oF thE FolloWing gEnERaL Formula (5-1) as well as the rEcUrring Units Of formula (4-1). 
HereIn k is as defINED above, R1 iS hydROgEN, methyl or CH2CO2R3, r2 is hyDrogen, methYL or CO2R3, R3 iS a strAight, braNched or cyCLIc alkyl gRouP of 1 To 15 cArbON AtOms, R4 is an acid lABIle gRoUp, R5 is seLecTed from AmoNg a HalOgeN aTom, a hydroXyl group, A sTrAiGhT, brAncheD Or cyclic AlKoxY
Herein R is hydrogen or astraight,branc hed  or  c ycli c al kyl group of 1 to 6  carbon atoms, example s ofwh i ch i n cl ude m ethyl,e th y l , n -p ro pyl ,i so propy l,n-butyl , sec-buty l,te rt-butyl, te r t- amyl, n-pe nty l, n-hexyl,cyc lopent yl , a n d cyc loh exyl.  W isa  singl e bond or  x e 2x80x9 4 (CH2)mx e 2 x8 0x94  in which one hyd r og e n atom may besubsti tu t ed w ith  ahydroxyl o raceto x y group ,  m i s  an integer from1 to 8, pre f era bly 1to  6. Illust rativ ee xam ples of W i nclu de a sing le bon d , methy l ene, et hylene , n -pr opyl e ne ,n-b ut y len e ,n-p e nty lene, n- he xy lene,  n-h e p t y lene , n -oct ylene , 1-hydroxy-n -pr opyl e ne,  1-ac etoxy -n-p ro pylen e, 2-h ydrox y- n-propylene, 2- acet oxy-n-pro pyl en e,1- hydro x y-n-bu tyl ene , 1-ace toxy-n- b uty le n e ,  2 -hydroxy-n-butylen e, 2 -a cetoxy-n -butyl e ne ,1 -hydroxy -n -pe ntyl e n e, 1- acet o xy -n-penty lene,2 -h yd roxy-n- pe ntylen e,  2- ace toxy- n -pen tylene , 4-hydr oxy-n - pentylene, 4-a c etoxy-n-penty l en e ,  1 - hydr oxy -n-hexylene , 1- a ceto xy-n - he xyl e ne, 2 -hydr ox y -n - hexylene, 2-acetoxy -n -hexyl ene,4-hydroxy-n-h exylene an d 4 -acetoxy -n-h e xy l ene. The lette r k i s 0 or 1,a nd n is2 or3.
Morespecifica l l y, the p oly mer s o f t h e  i nvention ared i vide dinto th e f ollowin g f our  su bge nu ses of po lymers.Su bg en us  (1 ) inc l udes pol ym ers  c omp risin g  recur ringunit sof the  follow i ng g ener al  f ormu la(5 -1) a s we l l a s the r ecurringuni t s of  f or mula (4 -1). 
Hereinkis as defi ne d a bove,R 1  is hydr ogen, methyl or CH2CO2R 3 , R2 is  hy droge n, m ethyl orCO2 R3, R3  is a stra ight,branc he d o r cycli c al kyl  g roup of 1t o  15  carb on  ato ms, R4is an acid labileg rou p, R5 is sele cte d fr o m  a mon g  a hal og e n a t o m, a hydroxyl g roup, a st ra i gh t, branche d  or  c yclic a lkoxy
Herein R_is hydrogen_or a straight, branched_or cyclic_alkyl_group of_1_to 6 carbon_atoms, examples of_which include methyl, ethyl,_n-propyl, isopropyl, n-butyl,_sec-butyl,_tert-butyl, tert-amyl, n-pentyl, n-hexyl, cyclopentyl, and cyclohexyl. W is a single bond or xe2x80x94(CH2)mxe2x80x94_in_which one_hydrogen_atom_may be substituted with a_hydroxyl or acetoxy group, m_is an_integer from 1 to 8, preferably 1 to_6._Illustrative examples of_W include a single bond, methylene, ethylene, n-propylene, n-butylene,_n-pentylene, n-hexylene, n-heptylene, n-octylene, 1-hydroxy-n-propylene, 1-acetoxy-n-propylene,_2-hydroxy-n-propylene, 2-acetoxy-n-propylene, 1-hydroxy-n-butylene,_1-acetoxy-n-butylene,_2-hydroxy-n-butylene,_2-acetoxy-n-butylene, 1-hydroxy-n-pentylene, 1-acetoxy-n-pentylene, 2-hydroxy-n-pentylene,_2-acetoxy-n-pentylene, 4-hydroxy-n-pentylene, 4-acetoxy-n-pentylene, 1-hydroxy-n-hexylene, 1-acetoxy-n-hexylene, 2-hydroxy-n-hexylene,_2-acetoxy-n-hexylene, 4-hydroxy-n-hexylene and 4-acetoxy-n-hexylene. The letter_k is 0 or 1, and n_is 2 or 3.
More specifically, the_polymers of the invention are_divided into_the following four subgenuses of_polymers.
Subgenus (1) includes_polymers comprising_recurring units of_the following general formula (5-1) as_well as the_recurring units of formula (4-1). 
Herein_k_is as defined_above,_R1_is hydrogen,_methyl or CH2CO2R3,_R2_is hydrogen,_methyl_or CO2R3, R3 is a straight,_branched_or cyclic alkyl group of 1 to_15 carbon atoms, R4_is_an acid labile group,_R5 is selected from among_a halogen atom, a hydroxyl group,_a straight,_branched or_cyclic alkoxy