The shapes and structures of grain boundaries formed between the basal (0001) surface of large alumina grains and randomly oriented small alumina grains are shown to depend on the additions of SiO2, CaO, and MgO. If a sapphire crystal is sintered at 1620degreesC in contact with high-purity alumina powder, the grain boundaries formed between the (0001) sapphire surface and the small alumina grains are curved and do not show any hill-and-valley structure when observed under transmission electron microscopy, (TEM). These observations indicate that the, grain boundaries are atomically rough. When 100 ppm (by mole) of SiO2 and 50 ppm of CaO are added, the (0001) surfaces of the single crystal and the elongated abnormal grains form flat grain boundaries with most of the fine matrix grains as observed at all scales including high-resolution TEM. These grain boundaries, which maintain their flat shape even at the triple junctions, are possible if and only if they are singular corresponding to cusps in the polar plots of the grain boundary energy as a function of the grain boundary normal. When MgO is added to the specimen containing SiO2 and CaO, the flat (0001) grain boundaries become curved at all scales of observation, indicating that they are atomically rough. The grain boundaries between small matrix grains also become defaceted and hence atomically rough.