Alumina as a polishing compound can be pretty fine so it won't put big scratched in stuff, but the individual particals are harder than hell. Got this off the web (diamond is 10 on the hardness scale):

RUBY, the red variety of corundum

VARIETY INFORMATION:
VARIETY OF: Corundum , Al2O3 .
USES: Gemstone.
BIRTHSTONE FOR: July
COLOR: various shades of red.
INDEX OF REFRACTION: 1.76 - 1.78
BIREFRINGENCE: 0.009
HARDNESS: 9
CLEAVAGE: none, although there is a rhombic parting
CRYSTAL SYSTEM: trigonal
PLEOCHROIC: strongly
SPECIMENS
Ruby is the red variety of corundum, the second hardest natural mineral known to mankind.