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Examples of this joining group include groups represented by general formulas (2) to (5) shown below. 

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In formulas (2) to (5), each of R 101 , R 102 , R 103 and R 104 independently represents a linear, branched or cyclic alkyl group of 1 to 12 carbon atoms, an aryl group, or a hydrogen atom, wherein the hydrogen atoms of the alkyl group or the aryl group may each be substituted with a halogen atom, an alkoxy group or an epoxy group. R $^{105 }$represents a linear, branched or cyclic alkylene group ofl to 12 carbon atoms, an arylene group, or a single bond, wherein the hydrogen atoms of the alkylene group or the arylene group may each be substituted with a halogen atom, an alkoxy group or an epoxy group. 

In the above general formulas (2) to (5), the alkyl group for R $^{101 }$to R $^{104 }$contains 1 to 12 carbon atoms, is preferably a linearor branched alkyl group, and is most preferably an ethyl group or a methyl group. 

The aryl group preferably contains 6 to 20 carbon atoms, and specific examples include a phenyl group and a naphthyl group. 

Examples of the halogen atom with which a hydrogen atom of the alkyl group or aryl group may be substituted include a fluorine atom, chlorine atom, bromine atom and iodine atom, and a fluorine atom is particularly desirable. 

The alkoxy group with which a hydrogen atom of the alkyl group or aryl group may be substituted preferably contains 1 to 5 carbon atoms, and is more preferably a methoxy group, ethoxy group, n-propoxy group, iso-propoxy group, n-butoxy group or tert-butoxy group. 

R $^{101 }$and R $^{102 }$are preferably both hydrogen atoms. 

R $^{103 }$and R $^{104 }$preferably both represent alkyl groups, rep› resent an alkoxy group and an alkyl group, or represent an alkoxy group and a hydrogen atom. 105 

In the general formula (5), R represents a linear, branched or cyclic alkylene group of 1 to 12 carbon atoms which may be substituted with an alkoxy group, hydroxyl group, halogen atom or epoxy group, an arylene group which may be substituted with an alkoxy group, hydroxyl group, halogen atom or epoxy group, or a single bond. 105 

Examples of the halogen atom within R include the same halogen atoms as those mentioned above within the description of R $^{101 }$ti R 104 . 

Examples of the alkoxy group within R $^{105 }$include the same 55 alkoxy groups as those mentioned above within the descrip› tion of R 101 to R 104 . 105 

Examples of the alkylene group or arylene group for R include groups in which a hydrogen atom has been removed from the alkyl groups and aryl groups described above for R $^{101 }$to R 104 . 

Of the above possibilities, R$^{105 }$is preferably an alkylene group or a single bond. 

Among the joining groups represented by the above gen- era! formulas (2) to (5), a joining group represented by the general formula (2) or a joining group represented by the 

general formula ( 4) is preferred, and a joining group repre› sented by the general formula (2) is the most desirable. 

Specific examples of preferred core portions of the poly- mer (C21) are shown below. 

[Chemical Formula 52] 

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(Arm Portions) 

The arm portions of the polymer (C21) are composed of polymer chains that are bonded to the core portion described above. 

These polymer chains that are bonded to the core portion are preferably bonded to each of the terminals of the core portion (namely, the terminals of X 21 on the opposite side from X $^{22 }$in the above formula (1 )). 

The polymer chains bonded to the core portion may be the same or different from each other, but are preferably the same, as such compounds yield superior effects for the present invention. 

Examples of the polymer chains that constitute the arm portions include the same polymers as those described above for the component (Cl). For example, specific examples of polymer chains containing the aforementioned structural units (a12) and (a32) include polymer chains containing the two structural units represented by general formula (P-1) shown below. 

