The invention provides a chemical-mechanical polishing composition containing a ceria abrasive, an ionic polymer of formula I: wherein X1 and X2, Z1 and Z2, R2, R3, and R4, and n are as defined herein, and water, wherein the polishing composition has a pH of about 1 to about 4.5. The invention further provides a method of chemically-mechanically polishing a substrate with the inventive chemical-mechanical polishing composition. Typically, the substrate contains silicon oxide, silicon nitride, and/or polysilicon.