An abrasive compound for a glass hard disk platter, characterized as comprising a stable slurry having water and, dispersed therein as an abrasive, cerium(IV) oxide particles having an average secondary particle size of 0.1 to 0.5 νm and containing CeO2 in a concentration of 0.2 to 30 wt %. Preferably, cerium accounts for 95 % or more in terms of oxides of the total amount of rare earth elements in the abrasive. The abrasive compound is suitable for polishing the surface of a glass substrate for an optical disk platter and a magnetic disk platter.