A crosslinked polymer or polymer fine particles which can be obtained through copolymerization of at least a macromonomer having a polyethylene glycol segment, a comonomer having tertiary amine groups in its side chains and a crosslinking agent are provided. Said crosslinked polymer can be provided in the form of polymer nano- or micro-spheres; and also as conjugate nano- or micro-spheres with their core parts fixing or encapsulating metal or semiconductor ultrafine particles.