To provide a polishing technique with which in production of a semiconductor integrated circuit device, when a plane to be polished is polished, an appropriate polishing rate ratio of a polysilicon film to another material can be obtained, whereby high level planarization of a plane to be polished including a polysilicon film can be realized. A polishing compound for chemical mechanical polishing, containing cerium oxide particles, a water-soluble polyamine and water and having a pH within a range of from 10 to 13, is used.